Geometry
Piscataway High School
Teacher:
Your Name
Email:
yourname@pway.org
Course Title: Honors Geometry / Geometry 9 / Geometry / Essentials of Geometry
Textbook:
Geometry (2014), HMH (Kanold, Burger, et al.)
Course Overview
Full year course: 5.0 credits (Honors Geometry has a 5 point weight added to the final grade)
Prerequisite: Algebra 1
Description: Geometry is a college prep course that uses constructions and transformations to explore
geometric relationships and figures. Students will use formal logic and various forms of proof in order
to explore topics such as congruence and similarity, properties of geometric shapes, measurement of
plane and solid figures, and trigonometry.
The Geometry course is structured as follows:
Unit
Topic
Length
Unit 1
Constructions and Introduction to Geometry
5 Days
Unit 2
Isometry and Transformations
12 Days
Unit 3
Introduction to Proof
10 Days
Unit 4
Triangles and Triangle Congruence
17 Days
Unit 5
Quadrilaterals and Coordinate Proofs
10 Days
Unit 6
Similarity
12 Days
Unit 7
Right Triangles and Trigonometry
17 Days
Unit 8
Circles
20 Days
Unit 9
Modeling in Three Dimensions
12 Days
1
Geometry Scope and Sequence
Unit
Timing
Topic
(1 day = 1 hour)
Concepts and Skills
Assessment for Unit 1 and 2 administered by the end of Cycle 4
Unit 1
5 Days
Constructions and
Introduction to
Geometry



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Unit 2
12 Days

Isometry and
Transformations



Identify basic geometry vocabulary (points, lines, planes, etc.)
Define terms related to constructions listed below
Constructions (with compass and straightedge, string, reflective devices, paper folding, and
technology)
Use formal geometric constructions (refer to summer project) and connect the definitions
learned in middle school to the constructions undertaken:
o Copy segment, copy angle, bisect segment, bisect angle, perpendicular lines, parallel
lines, perpendicular bisector, equilateral triangle, square, and hexagon in a circle
Use undefined terms such as points, lines and planes to create axiomatic system to build
other geometric terms (i.e. line segment, ray, angle, circle, etc.)
Transformations (Rigid Transformation)
o Perform transformations both on and off the coordinate plane
o Comparison to Linear Function transformations (i.e., which ones preserve distance and
angles and which do not?)
o Represent Transformations as taking points in the plane as inputs to others as outputs
o Translations (using vectors), reflections, and rotations using constructions and on the
coordinate plane
o Perform transformations to rectangles, parallelograms, trapezoids, and regular
polygons
o Use tracing paper investigations with ruler and protractor
Define congruence through Rigid Transformations on the coordinate plane and validate
using distance formula and midpoint formula
Composition of Transformations to identify congruence on the coordinate plane
Assessment for Unit 3 administered by the end of Cycle 6
Unit 3
10 Days

Introduction to
Proof


Discussion of logic and reasoning
o Use of Venn Diagrams to express conjunction and disjunction of sets
o Conditional, converse and bi-conditional statements
Discussion of proofs through rigid transformation
o Review properties of angles (vertical angles) and parallel line properties and
relationship to angles (corresponding, interior, exterior)
o Prove vertical angles are congruent
o Prove angle theorems related to parallel lines cut by a transversal
o Prove points on a perpendicular bisector equidistant from the endpoints of the segment
Using formal geometric constructions & transformations to help prove the above theorems
Assessment for Unit 4 administered by the end of Cycle 9
Unit 4
17 Days

Triangles and
Triangle
Congruence


Triangle Theorems
o Triangle Sum Theorem (using parallel lines)
o Isosceles Triangle Theorem (Base angle theorem) (using symmetry)
Inscribed and Circumscribed Triangles
o Construction of inscribed and circumscribed usual manual and digital tools
o Application of incenter and circumcenter
o Theorem: Medians of a Triangle meet at a point (prove using construction)
o Airport Problem
Triangle Congruence Theorems
o Corresponding Parts of Congruent Figures are Congruent (use transformations)
o AAS, ASA, SSS, SAS, HL congruence theorems
 Exploration of Coordinate Geometry
o Proofs (Given three points, prove the type of triangle)
Assessment for Unit 5 administered by the end of Cycle 11
Unit 5
10 Days
Quadrilaterals and
Coordinate Proofs




Use properties of quadrilaterals and other shapes in the coordinate plane
Proofs to determine the most specific name that can be given to a quadrilateral
Use distance formula and midpoint formula in proofs
Review and use slope of parallel and perpendicular lines in proofs
Geometry Scope and Sequence
Unit
Timing
Topic
(1 day = 1 hour)
Concepts and Skills
Assessment for Unit 6 administered by the end of Cycle 14
Unit 6
12 Days


Similarity


Discuss similarity through the definition of midsegments of a triangle
Discuss similarity through the use of dilations:
 Dilations completed from the origin and other points on coordinate plane
 Scale factor and center of dilation to explain similarity
 List corresponding parts (congruent or proportional)
 Finding the center of dilation given a dilation on a coordinate plane
 Subdivide a Segment in a Given Ratio (partition a line using different ratios)
Establish Triangle Similarity Postulates
o AA, SAS, SSS (prove using above discussions/activities)
o Prove proportionality theorems (include coordinate proofs)
Modeling: Using triangle similarity to solve problems through geometric relationships
Assessment for Unit 7 administered by the end of Cycle 17
Unit 7
17 Days
Right Triangles
and Trigonometry





Use similar triangles to define trigonometric ratios and their inverses in right triangles
o Demonstrate and apply relationship and sine and cosine of complementary angles
o Discuss range of trig ratios (e.g., certain ratios cannot have a value over 1)
Apply trigonometry and Pythagorean Theorem to solve word problems
o Use PARCC sample problems
o Use Lesson Performance Tasks in Module 13
Prove the Converse to the Pythagorean Theorem
Use the distance formula prove/demonstrate converses
Use distance formula to find area and perimeter of triangles (include trigonometry to find
altitudes of triangles)
Assessment for Unit 8 administered by the end of Cycle 21
Unit 8
20 Days

Circles






Review Constructions of inscribed and circumscribed polygons
o Prove properties of angles for a quadrilateral inscribed in a circle (opposite angles are
supplementary)
Review definition of Circles
Prove all circles are similar
Identify Circle relationships (See Circle Standard G-CA 2)
o Use relationships to prove facts about circles
Include informal discussion of area and perimeter of circumscribed polygons (limits, as the
number of sides increases what happens?)
Find arc length and sector area
o Include word problems
o Define radians
Use definition to derive equation of a circle
o Use Completing the Square to find radius and Center
NOTE – move equation of a circle first for PARCC.
Assessment for Unit 9 administered by the end of Cycle 23
Unit 9
12 Days
Modeling in Three
Dimensions



Discuss volume using Cavalieri’s Principle
o Informal limit process to find formulas
o Volume of prisms, pyramids, cones and spheres
o Volume of compound figures
Relationships between 2D and 3D Shapes
o Identify nets (Surface area) of cross sections
o Discuss conic sections
o Identify 3-D objects created by rotating 2-D objects
Complete word problems with 3-D shapes regarding surface area and volume
o Density; Designing packaging to maximize volume or minimize surface area