Escondido Union High School District
Informal Geometry
Course Length: One Year
UC/CSU Requirement:
Grade Level: 10 - 12
Graduation Requirement:
Does not meet UC/CSU Requirement
Fulfills 1 year of EUHSD math graduation
credit.
Course Number Semester 1: 7034 (P), 7065 (SE), 7074 (B)
Course Number Semester 2: 7035 (P), 7066 (SE), 7075(B)
Transcript Abbreviation: INFRML GEO A/B, SH INF GEO A/B, BAS INF GEOA/B
Number of Credits: 5 credits per semester
Prerequisite/s Required: Completion of Algebra I
Prerequisite/s Recommended: Grade of “D” in Algebra IA and/or Algebra IB
District Approved Instructional Materials/Textbook:
• McDougal Littell Geometry, Concepts and Skills. Copyright 2003 ISBN: 978-0618-501571
• Patty Paper – Michael Serra Publisher (Supplemental Suggested Resource)
• Geometry by Key Curriculum Press (Supplemental Suggested Resource)
• Making it Happen “EUHSD CAHSEE Review Binder” by Ignacio Ramirez and
Erin Duran
• Math Projects Journal (MPJ) by Chris Shore
Textbook Board Approval Date: 5/19/09
Curriculum Approval Date: 5/19/09
Course Description: The Informal Geometry course is designed as an informal
introduction to Geometry. All essential and expected California State Mathematics
Standards are taught and assessed with the exception of formal proof. There is a
consistent use and review of Algebra throughout the course. Basic definitions, postulates,
and theorems will be introduced in order for the student to use these in developing
deductive and inductive reasoning skills. Students will use and apply trigonometric
concepts to right triangles. Straightedge and compass constructions will be done
throughout the course as well as many applications to everyday life. The course also
includes a unit of study designed to prepare students for the California High School Exit
Exam. Students who wish to go on to another level of mathematics would take College
Preparatory Geometry as their next course of study.
(P) = College Preparatory; (SE) = Sheltered Instruction (B) = Basic
4/30/2009 2:55 PM
1
Units of Study
Informal Geometry
NOTE: Teachers in the Informal Geometry course are expected to follow the units of
study in a sequential order, however, due to the unique diversity of the students enrolled in
this course, it’s imperative that students receive differentiated instruction designed to
remediate their individual needs.
Suggested
Time
Unit
Frame
Common
Assessment
Weeks
Material Covered in
Class
Week 1
1st Semester (August - December)
Orientation and
1
Introduction to Course
Weeks 16
Unit 1: Tools of
Geometry
Weeks 7
- 10
Weeks 11
- 17
Week 18
Unit 2: Parallel and
Perpendicular Lines
Unit 3: Triangles
Ch 4 & 5
Weeks 1 3
Unit 4: CST/CAHSEE
Review (Data Analysis
and Probability)
3
Student Guide for
CAHSEE published by the
CDE.
Making It Happen
EUHSD Binder
Weeks 4
-8
Weeks 9
- 11
Weeks 12
- 15
Weeks 16
- 17
Week 18
Unit 5: Polygons,
Circles, and Area
Unit 6: Surface Area
and Volume
Unit 7: Similarity and
Transformations
5
Ch 6 & 8
3
Ch 9
4
Ch 7 and Transformations
2
Ch 10
Benchmark
1
6
McDougal Littell
Geometry, Concepts and
Skills (©2003)
Ch 1 & 2
4
Ch 3
Benchmark
7
2
Final Exam
nd
2 Semester (January – May)
Benchmark
3
Benchmark
4
Unit 8: Trigonometry
Final Exam
2
Orientation and Introduction to Course
Length of Study – 1 week
Orientation and Introduction to course will focus on the following topics and skills:
Topics Covered:
• Class Conduct
• Classroom Work Environment Procedures
• Course Requirements
• Vocabulary of Geometry
Skills Covered:
• Communication Skills – Listening/Speaking
• Note Taking
• Organizational Skills
• How to Use the Textbook Effectively and Efficiently
Student Learning Goal/Expected
Activity/Skill
Student Outcome
Students will be able to articulate the
Teacher will review course goals and
course goals and objectives for the
objectives.
Informal Geometry Course.
Students will be able to articulate the
Teacher will review classroom rules,
classroom conduct expectations, the
conduct, and behaviors.
materials used in the course and where
to locate them, and the course grading
Students will participate in class
policy.
discussion on rules, procedures, and
expectations.
Geometry Textbook Scavenger Hunt
Suggested Resources
Teacher Syllabus
Teacher Syllabus
Class Rules/Procedures
Teacher Syllabus
Class Rules/Procedures
Textbook pg 48
Orientation and Introduction to Course
Academic Content Vocabulary
Geometry, procedure consequence
3
Orientation and Introduction to Course
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Completion of required assignments
• Class participation
Unit 1
Tools of Geometry
Length of Study – 6 weeks
Unit 1 Overview: Tools of Geometry, will focus on the following topics and skills:
Topics Covered:
• Geometry Terminology (axioms, theorems, inductive and deductive reasoning)
• Construction of logical arguments with counterexamples
• Classifying figures and Problem Solving
• Performance of Basic Constructions
• Use of Coordinate Geometry
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Construct Line Segments and Angles
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
Prerequisite Skills Covered:
See Skills Review Handbook beginning on page 653. Solving Equations, Using Formulas, Simplify Radicals, Absolute Value, Translating
Word Problems into Expressions/Equations, Problem Solving
Prerequisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product, quotient),
expression, equation
4
State Geometry Standards – Unit 1
• G1.0: Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
• G3.0: Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
• G12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and
solve problems.
• G16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
• G17.0: Students prove theorems by using use coordinate geometry, including the midpoint of a line segment, the distance formula,
and various forms of equations of lines and circles.
Student Learning Goal/Expected
Activity/Skill
Suggested Resources
Student Outcome
Students will be able to identify and
Textbook Activity/Class Discussion
Textbook section 1.3
name points, lines, and planes.
Students will be able to sketch and name Textbook Activity/Class Discussion
Textbook section 1.4
intersections of lines and planes.
Students will be able to find the length
Textbook Activity/Class Discussion
Textbook section 1.5
of a segment by measuring.
Students will be able to name and
Textbook Activity 1.6 Kinds of Angles
Textbook section 1.6
classify an angle.
pg 34
Students will be able to find the
Textbook Activity/Class Discussion
Textbook section 2.1
midpoint of a segment using midpoint
formula.
Students will be able to find an angle
Textbook Activity 2.2 Folding Angle
Textbook section 2.2
measure using angle bisectors.
Bisectors pg 60
Students will be able to identify and find Textbook Activity/Class Discussion
Textbook section 2.3
complementary and supplementary
angles.
Students will be able to find the
Textbook Activity 2.4 Angles and
Textbook section 2.4
measurement of angles using vertical
Intersecting Lines pg 74
angles and linear pairs of angles.
Students will be able to identify parts of Textbook Activity/Class Discussion
Textbook section 2.5
an “if-then” statement.
Students will be able to identify
Textbook Activity/Class Discussion
Textbook section 1.2
inductive and deductive reasoning.
Textbook section 2.5
5
Students will be able to use
Textbook Activity/Class Discussion
Textbook section 1.2
counterexamples.
Chapter 1-2 Project Textbook pp102-103
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book.
Unit 1
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
acute angle, adjacent angles , angle bisector , bisect , bisector , complementary angles, conclusion , congruent angles, congruent
segments, conjecture , converse, coordinate , coplanar , counterexample, deductive reasoning , degree , distance , endpoint, hypothesis,
if-then-statement, inductive reasoning, intersect , intersection , length , line, linear pair , measure , midpoint, obtuse angle, plane , point ,
postulate, prediction , ray, right angle, segment , straight angle, supplementary angles, theorem, vertical angles
Unit 1
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
• District Benchmark Assessment 1
Unit 2
Parallel and Perpendicular Lines
Length of Study - 4 weeks
Unit 2 Overview: Parallel and Perpendicular Lines will focus on the following topics and skills:
Topics Covered:
• Parallel and Perpendicular Lines
• Parallel Lines Cut by a Transversal
• Slope of a Line
• Graphing Linear Equations
6
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Construct Parallel Lines
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
Pre-requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Slope, Translating Word Problems into
Expressions/Equations, Problem Solving
Pre-requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary, (sum, difference, product,
quotient), expression, equation, slope
Parallel and Perpendicular Lines Standards
• G7.0: Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals,
and the properties of circles.
• G16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
Student Learning Goal/Expected
Student Outcome
Students will be able to determine if
lines are parallel, perpendicular, or
skew.
Students will be able to find missing
angles using perpendicular and parallel
lines.
Students will be able to identify
corresponding, alternative interior,
alternative exterior, same-side interior,
and same-side exterior angles.
Activity/Skill
Suggested Resources
Textbook Activity 3.1 Lines in Space pg
107
Textbook Section 3.1
Textbook Activity/Class Discussion
Textbook Section 3.2
Textbook pp 126-127 Activity 3.4
Textbook Section 3.3
Parallel Lines and Angles – Students
Textbook Section 3.4
discover the relationships between
corresponding angles, alternating interior
angles, same side interior angles,
alternating exterior angles.
7
Students will be able to show why lines
are parallel using slope or parallel line
theorems.
Students will be able to name parallel
and perpendicular lines.
Students will be able to find the slope of
a line from two points or a linear
equation and will be able to graph linear
equations.
Textbook Activity/Class Discussion
Textbook Section 3.5
Textbook Section 3.6
Textbook Activity/Class Discussion
Textbook Section 3.1
Textbook Activity/Class Discussion
Textbook Skills Review pg. 665, 666, 667
Students will perform paper and pencil
constructions.
Constructions:
Patty Paper Geometry Key Curriculum Press
• Given point P on line k, construct
a line through P perpendicular to
k
• Given point R, not on line k,
construct a line through R,
perpendicular to k
• Given a line and a point,
construct a line through the point
parallel to the given line.
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book.
Unit 2
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
alternate exterior angles, alternate interior angles, construction, converse, corresponding angles, lines perpendicular to a plane, oblique
lines, parallel lines, parallel planes, perpendicular lines, same-side interior angles, skew lines, transversal
Unit 2
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
8
Unit 3
Triangles
Length of Study – 7 weeks
Unit 3 Overview: Triangles, will focus on the following topics and skills:
Topics Covered:
• Triangle Inequality Theorem
• Angle Sum Theorem
• Pythagorean Theorem
• Congruent triangles
• Corresponding parts of congruent triangles
Skills Covered:
• Listening/Speaking
• Organization
• Construct congruent triangles
• Individual and Group Work
• Conceptual Understanding
• Logic and Reasoning
Pre-Requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Radicals, Translating Word Problems into
Expressions/Equations, Using Formulas, Ratio and Proportion, Problem Solving
Pre-Requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product,
quotient), expression, equation , slope, ratio, proportion
Triangles Standards
• G5.0: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent
triangles.
• G6.0: Students know and are able to use the Triangle Inequality Theorem.
• G12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and
solve problems.
• G15.0: Students use the Pythagorean Theorem to determine distance and find missing lengths of sides of right triangles.
• G16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
9
Student Learning
Goal/Expected Student
Outcome
Students will be able to classify
triangles by their sides and
angles.
Students will be able to use the
Angle Sum Theorem for
triangles.
Students will be able to find
interior and exterior angles of
triangles.
Students will be able to find
angles and sides of isosceles and
equilateral triangles.
Students will be able to find a
missing side of a right triangle
using the Pythagorean theorem.
Students will be able to identify
corresponding angles and sides
of congruent triangles.
Students will be able to identify
which postulate shows triangles
are congruent.
Activity/Skill
Suggested Resources
Textbook Activity/Class Discussion
Textbook Section 4.1
Textbook Activity/Class Discussion
Textbook Section 4.2
Textbook Activity/Class Discussion
Textbook Section 4.2
Textbook Activity/Class Discussion
Textbook Section 4.3
Textbook Activity 4.4 Areas and Right Triangles pg 191
Textbook Section 4.4
Textbook Section 4.5
Website:
http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html
Interactive Pythagorean puzzle
Website:
http://argyll.epsb.ca/jreed/math8/strand3/3201.htm more
on Pythagorean Theorem
The America’s Cup Sail – Pythagorean Theorem, area of
trapezoid, midsegment of a trapezoid, parallel lines and
transversal corresponding angles
Shipping Conundrum – Pythagorean Theorem
Baseball Congruency – congruent triangles
Activity 5.2 Congruent Triangles (textbook pg. 240)
Internet
Internet
MPJ – Chris Shore
MPJ – Chris Shore
MPJ – Chris Shore
Textbook Section 5.1
Textbook Section 5.2
Textbook Section 5.3
10
Constructions:
Students will be able to
Textbook Section 4.7
determine whether lengths form
Patty Paper Geometry Key Curriculum
• Construct congruent triangles
a triangle (Triangle Inequality
Press
Theorem).
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book
Unit 3
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
acute triangle, alternate interior angles, altitude of a triangle, angle, angle bisector, base angles of a triangle, base of an isosceles triangle,
congruent figures, converse, corollary, corresponding parts of congruent figures, distance formula, equiangular triangle, equidistant,
equilateral triangle, exterior angles, hypotenuse, interior angles, isosceles triangle, leg of a right triangle, legs of an isosceles triangle,
median of a triangle, obtuse triangle, perpendicular bisector, proof, Pythagorean Theorem, right triangle, scalene triangle, triangle, vertex
of an angle, vertical angles
Unit 3
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
• District Benchmark 2
• Semester 1 Final Exam
11
Unit 4
CST/CAHSEE Review
(emphasis on Data Analysis and Probability)
Length of Study – 3 weeks
Unit 4 Overview: Operations on Rational Numbers, will focus on the following topics and skills:
Topics Covered:
• Ratio/Proportion
• Equation Solving
• Problem Solving
• Fractions/Decimals/Percents
• Discount Problems
• Statistics, Data Analysis, and Probability
• Graphing Linear Equations
• Interpreting Graphs
• Test Taking Skills
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
CST/CAHSEE Review Standards
CAHSEE Standards: See the CAHSEE Blueprint and released questions at http://www.cde.ca.gov/ta/tg/hs/resources.asp
12
Student Learning Goal/Expected
Student Outcome
Students will be able to show
understanding of measurements of
central tendency.
Students will be able to interpret data in
charts, tables and plots.
Students will be able to calculate the
probability of:
• Independent events
• Dependent Events
• Complement of an event
Activity/Skill
Suggested Resources
Students create and conduct a survey
and interpret results
Section 2 of Making It Happen
Interpret information from graphs in
newspapers (USA Today is good
source of colorful graphs)
Textbook Activity/Class Discussion
Newspapers or Internet
Section 3 of Making It Happen
Section 2 of Making It Happen
Unit 4
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
compare, contrast, correlation, data set, data, dependent events, describe, distribution, evaluate, events, explain , extremes of a,
proportion, favorable outcome , independent events, infer, mean, measure of central tendency, median, mode, outcome, outliers,
positive/negative correlation, possible outcome, prediction, probability, range of data set, relate, sample, scatter plot, summarize, support,
tree diagram, trial
Unit 4
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
13
Unit 5
Polygons, Circles and Area
Length of Study – 5 weeks
Unit 5 Overview: Polygons, Circles and Area, will focus on the following topics and skills:
Topics Covered:
• Classifying Polygons
• Finding angles of Polygons
• Area and Perimeter of Polygons
• Quadrilaterals and Their Properties
• Parts of the Circle
• Area and Circumference of Circles
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
Pre-Requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Translating Word Problems into
Expressions/Equations, Using Formulas, Problem Solving
Pre-Requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product,
quotient), expression, equation , slope, ratio, proportion
14
Polygons, Circles and Area Standards
• 7.0: Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals,
and the properties of circles.
• 8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of
common geometric figures.
• 10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and
trapezoids.
• 12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and
solve problems.
• 16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the
line parallel to a given line through a point off the line.
Student Learning Goal/Expected
Activity/Skill
Suggested Resources
Student Outcome
Students will be able to classify
Venn Diagram (flow chart, poster,
Textbook Section 6.1
polygons.
infomercial) to classify polygons
Textbook Section 8.1
especially quadrilaterals
Students will be able to identify angles
Textbook Activity/Class Discussion
Textbook Section 6.1
in polygons.
Students will be able to identify
Textbook Activity/Class Discussion
Textbook Section 6.1
congruent sides and angles in
quadrilateral.
Students will be able to determine
Textbook Activity 6.2 Investigating
Textbook Section 6.2
whether a quadrilateral is a
Parallelograms pg 309
Textbook Section 6.3
parallelogram.
Geo-Activity Making Parallelograms pg
316
Students will be able to identify
Textbook Technology Activity 6.3
Textbook Section 6.3
properties of quadrilaterals.
Making Parallelograms pg 324
Textbook Section 6.4
Textbook Section 6.6
Students will be able to find the
Textbook Activity/Class Discussion
Textbook Section 8.1
perimeter of a regular polygon.
Students will be able to find the
Textbook Activity 8.2 Angle Sum of
Textbook Section 8.2
measures of angles in regular polygons. Polygons pg 416
15
Students will be able to find the area of
a square, rectangle, parallelogram,
triangle, trapezoid, and composite
figures.
Textbook Activity 8.4 Finding Areas of
Triangles pg 430
Textbook Section 8.3
Textbook Section 8.4
Textbook Section 8.5
Textbook Section 8.6
MPJ:
MPJ – Chris Shore
•
•
•
The Gum Drop – area
Polygon House – area of
polygons, coordinate
geometry, trigonometric
functions, distance formula
Princess Dido and the Ox
Skin – area and perimeter
Students will be able to identify the
parts of a circle, diameter, radius,
circumference, and center.
Students will be able to find the
circumference and area of a circle.
Textbook Activity 8.7 Finding Area of
Circles pg 451
Textbook Section 8.7
A Slice of Pi – Circumference and Pi
MPJ – Chris Shore
Textbook Project Chapters 7-8 Designing a Park pp
468-469
Students will perform paper and pencil
construction.
Constructions:
• Construct a circle circumscribed
about a triangle
• Construct a circle inscribed in a
triangle
• Construct a “Golden Rectangle”
Patty Paper Geometry Key Curriculum Press
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book
16
Unit 5
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
area, base of a geometric figure, center of a circle, circle, circumference, concave polygon, convex polygon, diagonal of a polygon,
diameter, equiangular , equilateral, exterior angle, height of a figure, interior angle, parallelogram, perimeter, pi (π), polygon, radius,
rectangle, regular polygon, rhombus, semicircle, side of a polygon, square, trapezoid, vertex of a polygon
Unit 5
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
• District Benchmark 3
Unit 6
Surface Area and Volume
Length of Study – 3 weeks
Unit 6 Overview: Surface Area and Volume, will focus on the following topics and skills:
Topics Covered:
• Identify and Name 3-D Figures
• Surface Area and Volume of 3-D Figures
• Net Diagrams
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
17
Pre-Requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Translating Word Problems into
Expressions/Equations, Using Formulas, Problem Solving
Pre-Requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product,
quotient), expression, equation , slope, ratio, proportion
Surface Area and Volume Standards
• 8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of
common geometric figures.
• 9.0: Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to
memory the formulas for prisms, pyramids, and cylinders.
Student Learning Goal/Expected
Activity/Skill
Suggested Resources
Student Outcome
Students will be able to name solids
Textbook Activity/Class Discussion
Textbook Section 9.1
and identify their parts.
Students will be able to find the
Find surface area and volume of every day
Textbook Section 9.2
surface area and volume of prisms,
objects: cereal boxes, cans, classroom,
Textbook Section 9.3
cylinders, pyramids, cones, and
bedroom, etc
Textbook Section 9.4
spheres.
Textbook Section 9.5
Website:
http://www.learner.org/interactives/geometry/ Internet
Interactive application for finding area,
volume, and surface area
Textbook Activity 9.2 Investigating Surface
Area pp 481-482
Textbook Section 9.2
Textbook Activity 9.5 Investigating Volume
pp 508-509
Textbook Section 9.5
Swimming Pool – Measurement, Surface
area and volume of a rectangular and
trapezoidal prisms, Pythagorean Theorem
MPJ – Chris Shore
The Luxor – Pyramids, slant height, lateral
edge, surface area and volume, right triangle
trigonometry
MPJ – Chris Shore
18
The Shopkeepers Jar – Volume (cylinders
and spheres), circumference and diameter,
measurement, estimation
Super Size It! – Area and Volume of Prisms,
Fundamental Theorem of Similarity
Can There Be Giants? – Ratio of perimeter,
surface area and volume, writing algebraic
expressions
MPJ – Chris Shore
MPJ – Chris Shore
MPJ – Chris Shore
Shot Put Arc – Circles, lengths of Chords,
perpendicular bisector of a chord, arc length, MPJ – Chris Shore
trigonometric functions
Students will be able to identify nets
King Tut Deconstructing the Pyramids –
MPJ – Chris Shore
of solids.
Identifying and calculating the height, slant
height and lateral edge of a pyramid, surface
area and volume, right triangle trigonometry,
the relationship between a net and its solid
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book.
Unit 6
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
base of a geometric figure, cone, cylinder, edge, face of a polyhedron, height of a triangle, lateral area, lateral face, net (of a solid figure),
prism, pyramid, slant height , solid, sphere, surface area, volume
Unit 6
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
19
Unit 7
Similarity and Transformations
Length of Study – 4 weeks
Unit 7 Overview: Similarity and Transformations, will focus on the following topics and skills:
Topics Covered:
• Ratio and Proportion
• Similarity of Figures
• Translations
• Rotations
• Reflections
• Tessellations
• Symmetry
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
Pre-Requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Translating Word Problems into
Expressions/Equations, Using Formulas, Problem Solving, Ratio and Proportion
Pre-Requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product,
quotient), expression, equation , slope, ratio, proportion
Similarity and Transformations Standards
• 12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and
solve problems.
• 22.0: Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and
reflections.
20
Student Learning Goal/Expected
Student Outcome
Students will be able to solve ratios and
proportions.
Students will be able to calculate
distances using indirect measurement.
Students will be able to determine if
polygons are similar by using a scale
factor.
Students will be able to identify similar
sides using similarity statements.
Students will be able to use proportions
to solve for missing sides of similar
triangles.
Students will be able to find a scale
factor between similar figures.
Students will be able to identify if
figures are translations.
Students will be able to describe
translations.
Students will be able to describe
reflections.
Activity/Skill
Suggested Resources
Textbook Activity/Class Discussion
Textbook Section 7.1
Textbook Activity 7.2 Conjectures
About Similarity pg 364
Textbook Section 7.2
Textbook Activity/Class Discussion
Textbook Section 7.2
Textbook Activity/Class Discussion
Textbook Activity/Class Discussion
Textbook Section 7.3
Textbook Section 7.4
Textbook Section 7.5
Geo-Activity 7.6 Dilations pg 393
Textbook Section 7.6
How High: Do You Have the Inclination
– similar triangles
Textbook Activity/Class Discussion
MPJ – Chris Shore
Textbook Activity/Class Discussion
Textbook Section 3.7
Textbook Activity 5.7 Investigating
Reflections pg 281
Textbook Section 5.7
The Mason’s Secret – tessellations
MPJ – Chris Shore
Reflection Golf – transformations,
reflections, and composite reflections
MPJ – Chris Shore
Kaleidoscope - transformations,
reflections, and composite reflections
MPJ – Chris Shore
Textbook Section 3.7
21
William Tell – rotation by reflection
over two intersecting lines and rotation
of a figure around a given point
MPJ – Chris Shore
Textbook Project Chapters 5-6 Creating
Tessellations pp 352-353
Textbook pp 352-353
Have students create quilts using
transformations – paper or fabric
Textbook Activity/Class Discussion
Students will be able to draw and
Textbook Section 5.7
determine the number of lines of
symmetry.
Students will be able to compare
Textbook Activity/Class Discussion
Textbook Section 7.2
perimeter and area of similar polygons.
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book
Unit 7
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
extremes of a proportion, image, means of a proportion, pre-image, proportion, ratio, reflection, rotation, scale factor, similar polygons,
symmetry, transformation, translation
Unit 7
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
• District Benchmark 4
22
Unit 8
Trigonometry
Length of Study – 2 weeks
Unit 8 Overview: Trigonometry, will focus on the following topics and skills:
Topics Covered:
• Sine, Cosine, and Tangent Ratios
• Special Right Triangles
• Indirect Measurement
Skills Covered:
• Listening/Speaking
• Organization
• Individual and Group Work
• Mathematical Skills
• Conceptual Understanding
• Higher Level Thinking
• Logic and Reasoning
Pre-Requisite Skills: See Skills Review Handbook beginning on page 653 Solving Equations, Translating Word Problems into
Expressions/Equations, Using Formulas, Problem Solving, Radicals, Ratio
Pre-Requisite Vocabulary: variable, constant, coefficient, radical, absolute value, operation vocabulary (sum, difference, product,
quotient), expression, equation , slope radical, ratio, proportion
Trigonometry Standards
• G18.0: Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know
and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1.
• G19.0: Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length
of a side.
• G20.0: Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and
90° triangles and 45°, 45°, and 90° triangles.
23
Student Learning Goal/Expected
Activity/Skill
Student Outcome
Students will be able to find the tangent, Textbook Activity 10.4 Right Triangle
sine, and cosine ratios for right triangles. Ratio pg 556
Students will be able to find missing
sides and angles of right triangles using
trig ratios.
Students will be able to solve
application problems using trig ratios.
Indirect measurement of campus
landmarks Chapter 9-10 Project
How High: Surveyor’s Trig Trick
Suggested Resources
Textbook Section 10.4
Textbook Section 10.5
Textbook Section 10.6
Textbook pp 584-585
MPJ – Chris Shore
The America’s Cup Sail
Poison Weed
Polygon House
King Tut
The Luxor
Shot Put Arc
Students will be able to find sides of
right triangles using special right
triangles ratios.
Strike a Chord: Recognizing Pervasive
Patterns – Circles, lengths of chords,
perpendicular bisector of a chord, arc
length, trigonometric functions
Textbook Activity 10.3 Special Right
Triangles pg 548
Textbook Section 10.2
Textbook Section 10.3
How High: The Right Stuff – special
right triangles
MPJ – Chris Shore
Additional learning activities, technology activities, real-life applications, and projects available in each chapter resource book
24
Unit 8
Academic Content Vocabulary
Note: All academic vocabulary definitions can be found in the appendix of this document.
cosine, hypotenuse, leg of a right triangle , radical, radicand, sine, tangent, trigonometric ratio
Unit 8
Assessment
Students will be assessed through a variety of measures including, but not limited to:
• Informal assessments: warm-up, assignments, projects, notebooks
• Teacher created/publisher provided formative assessments
• Teacher created/publisher provided summative assessments
• Semester 2 Final Exam
25
Appendix A
Vocabulary and Definitions
Vocabulary
Definition
acute angle
An angle with measure between 0° and 90°.
A number's distance from zero on the number line. The absolute value of -4
absolute value
is 4; the absolute value of 4 is 4. |-8| = 8
acute triangle
A triangle with three acute angles.
adjacent angles
Two angles with a common vertex and side but no common interior points.
alternate exterior
For two lines intersected by a transversal, a pair of angles that lie on opposite
angles
sides of the transversal and outside the other two lines.
alternate interior
For two lines intersected by a transversal, a pair of nonadjacent angles that
angles
lie on opposite sides of the transversal and between the other two lines.
A perpendicular segment from a vertex to the line containing the opposite
altitude of a triangle
side.
Consists of two rays with the same endpoint. The rays are the sides of the
angle
angle, and the endpoint is the vertex of the angle.
angle bisector
A ray that divides an angle into two angles that are congruent.
area
The amount of surface covered by a figure.
base of a geometric
A side of a polygon; a face of a three-dimensional figure by which the figure
figure
is measured or classified.
base angles of a
One of the two angles that have the base of the triangle as a side.
triangle
base of an isosceles
One of the two angles that have the base of the triangle as a side.
triangle
bisect
To divide into two congruent parts.
bisector
A straight line which bisects an angle or segment.
The point inside a circle that is the same distance from every point on the
center of a circle
circle.
The set of all points in a plane that are the same distance from a given point,
circle
called the center of the circle.
circumference
The distance around a circle.
coefficient
A number multiplied by a variable.
compare
To decide the relationship of two or more values or geometrical shapes.
complementary angles Two angles whose measures have a sum of 90°
A polygon in which a diagonal can be drawn such that part of the diagonal
concave polygon
contains points in the exterior of the polygon.
The “then” part of an if-then statement. In the statement “If it is cold, then I
conclusion
will wear my coat,” the conclusion is “I will wear my coat.”
A solid with a circular base and a vertex that is not in the same plane as the
base. The height of a cone is the perpendicular distance between the vertex
cone
and the base. The radius of a cone is the radius of the base. The slant height
of a cone is the distance between the vertex and a point on the base edge.
congruent angles
Angles that have the same measure.
26
Vocabulary
congruent figures
congruent segments
conjecture
constant
construction
contrast
converse
convex polygon
coordinate
coplanar
corollary
correlation
correlation (negative)
correlation (positive)
corresponding angles
corresponding parts of
congruent figures
cosine
counterexample
cylinder
data
data set
deductive reasoning
degree
dependent events
describe
diagonal of a polygon
Definition
Two geometric figures that have exactly the same size and shape. When two
figures are congruent, all pairs of corresponding angles and corresponding
sides are congruent.
Segments that have the same length.
An unproven statement that is based on a pattern or observations.
A value that does not change.
A geometric drawing that uses a limited set of tools, usually a compass and a
straightedge.
To compare in order to show unlikeness or differences, note the opposite
natures, purposes, etc.
The statement formed by switching the hypothesis and the conclusion of an
if-then statement.
A polygon is convex if no line that contains a side of the polygon passes
through the interior of the polygon.
The real number that corresponds to a point on a line.
Points that lie in the same plane.
A theorem whose proof follows directly from another theorem.
A measure of the strength and direction of the relationship between two
variables or data sets.
Two data sets have a negative correlation if one set of data values increases
as the other set decreases.
Two data sets have a positive correlation if both sets of data values increase.
Two angles that are formed by two lines and a transversal, and occupy
corresponding positions.
The corresponding sides and angles in congruent figures.
A trigonometric ratio, abbreviated as cos and computed as the ratio of the
length of the leg adjacent to the angle to the length of the hypotenuse.
An example that shows that a conjecture is false.
A solid with two congruent circular bases that lie in parallel planes. The
height of a cylinder is the perpendicular distance between the bases. The
radius of the cylinder is the radius of a base.
Information gathered from a survey or experiment.
Set of numbers and/or values can be represented in stem-and-leaf plots, line
plots, box-and-whisker plots, etc.
Using facts, definitions, accepted properties, and the laws of logic to make a
logical argument.
1
A unit of angle measure; one degree is 360 of a circle.
Events for which the occurrence or nonoccurrence of one event affects the
probability of the other event.
To tell or depict in written or spoken words.
A segment connecting two nonconsecutive vertices of a polygon.
27
Vocabulary
diameter
difference
distance
distance formula
distribution
edge
endpoint
equation
equiangular
equiangular triangle
equidistant
equilateral
equilateral triangle
evaluate
event
explain
expression
exterior angle
extremes of a
proportion
face of a polyhedron
favorable outcome
height of a triangle
hypotenuse
hypothesis
if-then-statement
image
independent events
inductive reasoning
infer
interior angle
intersect
Definition
The distance across the circle, through the center. The diameter is twice the
radius. A chord that passes through the center of the circle is also called a
diameter.
The answer to a subtraction problem.
A linear dimension that is always non-negative; the space between two
points or objects.
In the coordinate plane, the distance from (x1, - x1) is d = d =√ (x2 – x1)2 + (Y2 –
y1)2.
The frequency of occurrence of any item or category of items.
A segment that is the intersection of two faces of a polyhedron.
A point at an end of a segment or the starting point of a ray.
A mathematical statement that two expressions are equal.
Having all the angles equal.
A triangle with three congruent angles.
The same distance.
Having all the sides equal: an equilateral triangle.
A triangle with three congruent sides.
To find the value of an algebraic expression by substituting a number for
each variable and simplifying by using the order of operations.
An outcome or set of outcomes in a probability experiment.
Interpret your answer, justify the steps used in a solution.
A mathematical phrase that contains operations, numbers, and/or variables.
The angle between any side of a polygon and an adjacent side.
a c
The extremes of the proportion b = d are a and d.
A flat surface of the polyhedron.
The occurrence of one of several possible outcomes of a specified event or
probability experiment.
A segment from a vertex that forms a right angle with a line containing the
base.
In a right triangle, the side opposite the right angle. The hypotenuse is the
longest side of a right triangle.
The “if” part of an if-then statement. In the statement “If it is cold, then I
will wear my coat,” the hypothesis is “it is cold.”
A statement with two parts: an “if” part that contains the hypothesis and a
“then” part that contains the conclusion.
The new figure that results from the transformation of a figure in a plane.
Events for which the occurrence or nonoccurrence of one event does not
affect the probability of the other event.
A process that includes looking for patterns and making conjectures.
To conclude, to deduce, to reason.
The angle formed inside a polygon by two adjacent sides.
Figures intersect if they have any points in common.
28
Vocabulary
intersection
isosceles triangle
lateral area
lateral face
leg of a right triangle
leg of an isosceles
triangle
length
line
linear pair
line perpendicular to a
plane
mean
means of a proportion
measure
measure of central
tendency
median
median of a triangle
midpoint
mode
net (of a solid figure)
oblique lines
obtuse angle
obtuse triangle
operation
outcome
outliers
parallel lines
parallel planes
parallelogram
perimeter
Definition
The intersection of two or more figures is the point or points that the figures
have in common.
A triangle with at least two congruent sides.
The sum of the areas of the lateral faces of a prism or pyramid, or the area of
the lateral surface of a cylinder or cone.
A face of a prism or a pyramid that is not a base.
The sides that form the right angle (not the hypotenuse).
One of the two congruent sides of the isosceles triangle.
The distance between the two endpoints of a segment.
A line has one dimension and extends without end in two directions. It is
represented by a line with two arrowheads.
Two adjacent angles whose noncommon sides are on the same line.
A line that intersects a plane in a point and is perpendicular to every line in
the plane that intersects it.
The sum of all the values in a data set divided by the number of data values.
Also called the average.
a c
In the proportion b = d , b and c are the means. If the proportion is written
as a:b = c:d, the means are in the two middle positions.
The size or length of something.
A measure that describes a data set.
For an ordered data set with an odd number of values, the median is the
middle value. For an ordered data set with an even number of values, the
median is the average of the two middle values.
A segment whose endpoints are a vertex of the triangle and the midpoint of
the opposite side.
The point on a segment that divides it into two congruent segments.
The value or values that occur most frequently in a data set; if all values
occur with the same frequency, the data set is said to have no mode.
A diagram of the faces of a three-dimensional figure arranged in such a way
that the diagram can be folded to form the three-dimensional figure.
Lines that are neither perpendicular nor parallel.
An angle that measures greater than 90° and less than 180°.
A triangle with one obtuse angle.
Mathematical processes such as addition, subtraction, multiplication and
division.
A possible result of a probability experiment.
A data value that is far removed from the rest of the data.
Two lines that lie in the same plane and do not intersect.
Two planes that do not intersect.
A quadrilateral with both pairs of opposite sides parallel.
The sum of the side lengths of a closed plane figure.
29
Vocabulary
perpendicular bisector
perpendicular lines
pi (π)
plane
point
polygon
possible outcome
postulate
prediction
pre-image
prism
probability
product
proof
proportion
pyramid
Pythagorean Theorem
quotient
radical
radicand
radius
range of a data set
ratio
ray
rectangle
reflection
Definition
A line that is perpendicular to a segment at its midpoint.
Two lines that intersect to form a right angle.
The ratio of the circumference of a circle to its diameter. Pi is an irrational
number denoted by π and is approximately equal to 3.14.
A plane has two dimensions. It is represented by a shape that looks like a
floor or wall. You have to imagine that it extends without end, even though
the drawing of a plane appears to have edges.
A point has no dimension. It is represented by a small dot.
A plane figure that is formed by three or more segments called sides. Each
side intersects exactly two other sides at each of its endpoints. Each
endpoint is a vertex of the polygon.
One of the possible results that can happen in an experimental probability
trial; the sample space is all the possible outcomes.
A statement that is accepted without further justification.
A reasonable guess as to what will most likely occur from a given situation.
The original figure in a transformation.
A polyhedron with two congruent faces, called bases that lie in parallel
planes. The other faces are called lateral faces. The height is the
perpendicular distance between the bases.
A number from 0 to 1 (or 0% to 100%) that is the measure of how likely an
event is to occur.
The result obtained by multiplying two or more quantities together.
A convincing argument that shows why a statement is true.
a
c
An equation that states that two ratios are equal. Example: b = d
A polyhedron in which the base is a polygon and the lateral faces are
triangles with a common vertex.
For any right triangle, if the legs have lengths a and b and the hypotenuse has
length c, then a²+b²=c².
The number obtained by dividing one quantity by another. In 45 ÷3=15, 15
is the quotient.
A mathematical expression indicating a root, written with a radical
.
symbol
The number or expression written inside a radical symbol. In the radical
25, the radicand is 25.
The distance from the center to a point on the circle. A segment whose
endpoints are the center of the circle and a point on the circle is also called a
radius. The plural of radius is radii.
The difference of the greatest and least values in the data set.
A comparison of two quantities by division.
A part of a line that starts at an endpoint and extends forever in one direction.
A parallelogram with four right angles.
A transformation that creates a mirror image. The original figure is reflected
in a line of reflection.
30
Vocabulary
regular polygon
relate
rhombus
right angle
right triangle
rotation
same-side interior
angles
sample
scale factor
scalene triangle
scatter plot
segment
semicircle
side of a polygon
similar polygons
sine
skew lines
slant height of a
regular pyramid
slant height of a right
cone
slope
solid
sphere
square
straight angle
sum
summarize
supplementary angles
support
surface area
symmetry
Definition
A polygon that is both equilateral and equiangular.
Show a connection between two or more units.
A parallelogram with four congruent sides.
An angle that measures 90°.
A triangle with one right angle.
A transformation in which a figure is turned about a fixed point, called the
center of rotation. Rays drawn from the center of rotation to a point and its
image form an angle called the angle of rotation.
Two angles that are formed by two lines and a transversal, and lie between
the two lines on the same side of the transversal.
A part of a group being surveyed.
The radio of the lengths of two corresponding sides of two similar polygons.
A triangle with no congruent sides.
A graph with points plotted to show a possible relationship between two sets
of data.
Part of a line that consist of two points, called endpoints, and all points on
the line that are between the endpoints.
An arc whose central angle measures 180°.
One of the segments that form a polygon.
Two polygons are similar polygons if corresponding angles are congruent
and corresponding side lengths are proportional. The symbol for “is similar
to” is ~.
A trigonometric ratio, abbreviated as sin and computed as the ratio of the
length of the leg opposite the angle to the length of the hypotenuse.
Two lines that do not lie in the same plane and do not intersect.
The distance from the vertex of a regular pyramid to the midpoint of an edge
of the base.
The distance from the vertex of a right cone to a point on the edge of the
base.
The ratio of the vertical change (rise) to the horizontal change (run) between
any two points on a line.
A three-dimensional shape.
The set of all points in space that are the same distance from a point, called
the center of the sphere. The radius of a sphere is the length of a segment
from the center to a point on the sphere.
A parallelogram with four congruent sides and four right angles.
An angle with measure 180°.
The result of adding two or more numbers together.
Restate briefly the important facts of a problem or solution.
Two angles whose measures have a sum of 180°.
To uphold, support your conclusion.
The total area of all faces and curved surfaces of a three-dimensional figure.
In the transformation of a figure such that the image coincides with the preimage, the image and pre-image have symmetry.
31
Vocabulary
tangent
theorem
transformation
translation
transversal
trapezoid
tree diagram
trial
triangle
trigonometric ratio
variable
vertex of an angle
vertex of a polygon
vertical angles
volume
Definition
A line in the plane of a circle that intersects the circle in exactly one point,
called a point of tangency.
A true statement that follows from other true statements.
An operation that maps, or moves, a figure onto an image.
A transformation that slides each point of a figure the same distance in the
same direction.
A line that intersects two or more coplanar lines at different points.
A quadrilateral with exactly one pair of parallel sides, called bases. The
nonparallel sides are the legs.
A branching diagram that shows all possible combinations or outcomes of an
experiment.
In probability, a single repetition or observation of an experiment.
A figure formed by three segments joining three non-collinear points, called
vertices. The triangle symbol is ∆.
A ratio of the lengths of two sides of a right triangle.
A symbol used to represent a quantity that can change.
The common endpoint of the sides of the angle.
The intersection of two sides of the polygon.
The nonadjacent angles formed by two intersecting lines.
The number of non-overlapping unit cubes of a given size that will exactly
fill the interior of a three-dimensional figure.
32
Appendix B
Geometry CST Blueprint and Released items
CALIFORNIA CONTENT STANDARDS: GEOMETRY
# of
Items
%
65
100%
The geometric skills and concepts in this discipline are useful to all
students. Aside from learning these skills and concepts, students will
develop their ability to construct formal, logical arguments and
proofs in geometric settings and problems.
Geometry
1.0* Students demonstrate understanding by identifying and
giving examples of undefined terms, axioms, theorems,
and
inductive and deductive reasoning.
2.0* Students write geometric proofs, including proofs by
contradiction.
3.0* Students construct and judge the validity of a logical
argument and give counterexamples to disprove a statement.
4.0* Students prove basic theorems involving congruence and
similarity.
5.0
Students prove that triangles are congruent or similar, and they
are able to use the concept of corresponding parts of congruent
triangles.
6.0
Students know and are able to use the triangle inequality
theorem.
7.0* Students prove and use theorems involving the properties of
parallel lines cut by a transversal, the properties of
quadrilaterals, and the properties of circles.
8.0* Students know, derive, and solve problems involving
perimeter, circumference, area, volume, lateral area, and
surface area of common geometric figures.
9.0
Students compute the volumes and surface areas of prisms,
pyramids, cylinders, cones, and spheres; and students commit to
memory the formulas for prisms,
pyramids, and cylinders.
10.0* Students compute areas of polygons, including rectangles,
scalene triangles, equilateral triangles, rhombi,
parallelograms, and trapezoids.
11.0 Students determine how changes in dimensions affect the
perimeter, area, and volume of common geometric figures and
solids.
2
3
4
5
2
1
5 2/3**
4
2
4
1
33
CALIFORNIA CONTENT STANDARDS: GEOMETRY
12.0* Students find and use measures of sides and of interior
and
exterior angles of triangles and polygons to classify
figures and
solve problems.
13.0 Students prove relationships between angles in polygons
by
using properties of complementary, supplementary,
vertical, and
exterior angles.
14.0* Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine
distance and
find missing lengths of sides of right
triangles.
16.0* Students perform basic constructions with a straightedge and
compass, such as angle bisectors, perpendicular
bisectors,
and the line parallel to a given line through a point off the line.
17.0* Students prove theorems by using coordinate geometry,
including the midpoint of a line segment, the distance
formula, and various forms of equations of lines and
circles.
18.0* Students know the definitions of the basic trigonometric
functions defined by the angles of a right triangle. They
also
know and are able to use elementary relationships
between
them. For example, tan(x) = sin(x)/cos(x), (sin (x))2 + (cos (x))2 =
1.
19.0* Students use trigonometric functions to solve for an
unknown length of a side of a right triangle, given an angle
and a length of a side.
20.0 Students know and are able to use angle and side
relationships in problems with special right triangles, such as
30°, 60°, and 90° triangles and 45°, 45°, and 90°
triangles.
21.0* Students prove and solve problems regarding relationships
among chords, secants, tangents, inscribed angles, and
inscribed and circumscribed polygons of circles.
22.0* Students know the effect of rigid motions on figures in the
coordinate plane and space, including rotations,
translations,
and reflections.
GEOMETRY TOTAL
# of
Items
%
5
2
1/3**
2
4
3
3
3
1
5
3
65
100%
34