Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
Curriculum Map
Course Title: Geometry Honors
Quarter: 1
Academic Year: 2012-2013
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
Chapter 1
Foundations in
Geometry
1.1 Understanding Points,
Lines, and Planes
1.2 Measuring and
Constructing Segments
1.3 Measuring and
Constructing Angles
1.4 Pairs of Angles
1.5 Using Formulas in
Geometry
1.6 Midpoint and
Distance in the
Coordinate Plane
1.7 Transformations in
the Coordinate Plane
Chapter 2 Geometric
Reasoning
2.1 Using Inductive
Reasoning to Make
Conjectures
Standards
State Standards
G.1.1
G.1.2
G.1.3
G.1.4
G.1.5
G.1.7
G.2.4
G.5.1
G.5.3
G.5.4
G.7.1
Content
Apply basic facts
about points, lines,
planes, segments,
and angles.
Measuring and
constructing
segments and
angles.
Using formulas to
find distance and
the coordinates of a
midpoint.
Skills







Common Core
Standards
CC.9-12. G.CO.1
CC.9-12.G.CO.2
CC.9-12.G.CO.5
CC.9-12.G.CO.9
CC.9-12.G.CO.10
CC.9-12.G.CO.11
CC.9-12.G.CO.12
CC.9-12.A.SSE.1
Identifying
reflections,
rotations, and
translations.
Inductive and
deductive
reasoning.
Using conditional
statements and
biconditional
statements.





Identify, name, and draw
points, lines, segments, rays,
and planes.
Apply basic facts about points,
lines, and planes
Use length and midpoint of a
segment.
Construct midpoints and
congruent segments.
Name and classify angles.
Measure and construct angles
and angle bisectors.
Identify adjacent, vertical,
complementary, and
supplementary angles.
Find measures of pairs of angles.
Apply formulas for perimeter,
area, and circumference.
Develop and apply the formula for
midpoint.
Use the Distance Formula and the
Pythagorean Theorem to find the
distance between two points.
Identify reflections, rotations, and
translations.
Assessment
Textbook
assignments
Worksheet
assignments
Notebooks
Quizzes
Tests
Oral Responses
Resources
Textbook: Holt
McDougal
Geometry
Common Core
2012 Edition
Textbook Prentice
Hall Geometry
1998 Edition
Textbook
McDougal Littell
Geometry 2004
Edition
Observations
Intro to Geometry
Frank Schaffer
Publications
Teacher generated
worksheets
PowerPoint
Presentations
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
Curriculum Map
Course Title: Geometry Honors
Quarter: 1
Academic Year: 2012-2013
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
2.2 Conditional
Statements
2.3 Using Deductive
Reasoning to Verify
Conjectures
2.4 Biconditional
Statements and
Definitions
2.5 Algebraic Proof
2.6 Geometric Proof
2.7 Flowchart and
Paragraph Proofs
Chapter 3 Parallel and
Perpendicular
Lines(part 1)
3.1 Lines and Angles
3.2 Angles Formed by
Parallel Lines and
Transversals
3.3 Proving Lines Parallel
3.4 Perpendicular Lines
Standards
CC.9-12.A.CED.4
CC.9-12.G.GPE.7
CC.9-12.G.SRT.4
Standards for
Mathematical Practice
SMP1
SMP2
SMP3
SMP4
SMP5
SMP6
SMP7
SMP8
Content
Skills

Justifying solutions
to algebraic
equations.
Writing two-column,
flowchart, and
paragraph proofs.
Parallel and
perpendicular lines.
Angles formed by
parallel lines and a
transversal










Graph transformations in the
coordinate plane.
Use inductive reasoning to
identify patterns and make
conjectures.
Find counterexamples to disprove
conjectures.
Identify, write, and analyze the
truth value of conditional
statements.
Write the inverse, converse, and
contrapositive of a conditional
statement.
Apply the Law of Detachment and
the Law of Syllogism in logical
reasoning.
Write and analyze biconditional
statements.
Review properties of equality and
use them to write algebraic
proofs.
Identify properties of equality and
congruence.
Write two-column proofs.
Prove geometric theorems by
using deductive reasoning.
Assessment
Resources
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
Curriculum Map
Course Title: Geometry Honors
Quarter: 1
Academic Year: 2012-2013
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
Standards
Content
Skills







Write flowchart and paragraph
proofs.
Prove geometric theorems by
using deductive reasoning.
Identify parallel, perpendicular,
and skew lines.
Identify the angles formed by two
lines and a transversal.
Prove and use theorems about
the angles formed by parallel lines
and a transversal.
Use the angles formed by a
transversal to prove two lines are
parallel.
Prove and apply theorems about
perpendicular lines.
Assessment
Resources
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
State Standards
G.1: Students find lengths and midpoints of line segments. They describe and
use parallel and perpendicular lines. They find slopes and equations of lines.
G.1.1: Find the lengths and midpoints of line segments in one- or two-dimensional
coordinate systems.
G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and
perpendicular lines using a straight edge and compass, explaining and justifying the
process used.
G.1.3: Understand and use the relationships between special pairs of angles formed
by parallel lines and transversals.
G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines,
and equations of lines.
G.2: Students identify and describe polygons and measure interior and
exterior angles. They use congruence, similarity, symmetry, tessellations, and
transformations. They find measures of sides, perimeters, and areas.
G.2.2: Find measures of interior and exterior angles of polygons, justifying the
method used.
G.2.3: Use properties of congruent and similar polygons to solve problems.
G.2.4: Apply transformations (slides, flips, turns, expansions, and contractions) to
polygons in order to determine congruence, similarity, symmetry, and tessellations.
Know that images formed by slides, flips and turns are congruent to the original
shape.
G.2.5: Find and use measures of sides, perimeters, and areas of polygons, and
relate these measures to each other using formulas.
G.2.6: Use coordinate geometry to prove properties of polygons such as regularity,
congruence, and similarity.
G.3: Students identify and describe simple quadrilaterals. They use
congruence and similarity. They find measures of sides, perimeters, and
areas.
G.3.1: Describe, classify, and understand relationships among the quadrilaterals
square, rectangle, rhombus, parallelogram, trapezoid, and kite.
G.3.2: Use properties of congruent and similar quadrilaterals to solve problems
involving lengths and areas.
G.3.3: Find and use measures of sides, perimeters, and areas of quadrilaterals, and
relate these measures to each other using formulas.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
G.3.4: Use coordinate geometry to prove properties of quadrilaterals such as
regularity, congruence, and similarity.
G.4: Students identify and describe types of triangles. They identify and draw
altitudes, medians, and angle bisectors. They use congruence and similarity.
They find measures of sides, perimeters, and areas. They apply inequality
theorems.
G.4.1: Identify and describe triangles that are right, acute, obtuse, scalene,
isosceles, equilateral, and equiangular.
G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, and
perpendicular bisectors.
G.4.3: Construct triangles congruent to given triangles.
G.4.4: Use properties of congruent and similar triangles to solve problems involving
lengths and areas.
G.4.5: Prove and apply theorems involving segments divided proportionally.
G.4.6: Prove that triangles are congruent or similar and use the concept of
corresponding parts of congruent triangles.
G.4.7: Find and use measures of sides, perimeters, and areas of triangles, and
relate these measures to each other using formulas.
G.4.8: Prove, understand, and apply the inequality theorems: triangle inequality,
inequality in one triangle, and hinge theorem.
G.4.9: Use coordinate geometry to prove properties of triangles such as regularity,
congruence, and similarity.
G.5: Students prove the Pythagorean Theorem and use it to solve problems.
They define and apply the trigonometric relations sine, cosine, and tangent.
G.5.1: Prove and use the Pythagorean Theorem.
G.5.2: State and apply the relationships that exist when the altitude is drawn to the
hypotenuse of a right triangle.
G.5.4: Define and use the trigonometric functions (sine, cosine, tangent, cosecant,
secant, cotangent) in terms of angles of right triangles.
G.5.5: Know and use the relationship sin²x + cos²x = 1.
G.5.6: Solve word problems involving right triangles.
G.6: Students define ideas related to circles: e.g., radius, tangent. They find
measures of angles, lengths, and areas. They prove theorems about circles.
They find equations of circles.
G.6.2: Define and identify relationships among: radius, diameter, arc, measure of an
arc, chord, secant, and tangent.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
G.6.3: Prove theorems related to circles.
G.6.5: Define, find, and use measures of arcs and related angles (central, inscribed,
and intersections of secants and tangents).
G.6.6: Define and identify congruent and concentric circles.
G.6.7: Define, find, and use measures of circumference, arc length, and areas of
circles and sectors. Use these measures to solve problems.
G.6.8: Find the equation of a circle in the coordinate plane in terms of its center and
radius.
G.7: Students describe and make polyhedra and other solids. They describe
relationships and symmetries, and use congruence and similarity.
G.7.2: Describe the polyhedron that can be made from a given net (or pattern).
Describe the net for a given polyhedron.
G.7.4: Describe symmetries of geometric solids.
G.7.5: Describe sets of points on spheres: chords, tangents, and great circles.
G.7.6: Identify and know properties of congruent and similar solids.
G.7.7: Find and use measures of sides, volumes of solids, and surface areas of
solids, and relate these measures to each other using formulas.
G.8: Mathematical Reasoning and Problem Solving
G.8.6: Identify and give examples of undefined terms, axioms, and theorems, and
inductive and deductive proof.
G.8.8: Write geometric proofs, including proofs by contradiction and proofs involving
coordinate geometry. Use and compare a variety of ways to present deductive
proofs, such as flow charts, paragraphs, and two-column and indirect proofs.
Common Core Standards
Congruence G-CO
Experiment with transformations in the plane
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
2. Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as
inputs and give other points as outputs. Compare transformations that preserve
distance and angle to those that do not (e.g., translation versus horizontal stretch).
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and line segments.
5. Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motions
6. Use geometric descriptions of rigid motions to transform figures and to predict the
effect of a given rigid motion on a given figure; given two figures, use the definition
of congruence in terms of rigid motions to decide if they are congruent.
7. Use the definition of congruence in terms of rigid motions to show that two
triangles are congruent if and only if corresponding pairs of sides and corresponding
pairs of angles are congruent.
8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from
the definition of congruence in terms of rigid motions.
Prove geometric theorems
9. Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular
bisector of a line segment are exactly those equidistant from the segment’s
endpoints.
10. Prove theorems about triangles. Theorems include: measures of interior angles
of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and
half the length; the medians of a triangle meet at a point.
11. Prove theorems about parallelograms. Theorems include: opposite sides are
congruent, opposite angles are congruent, the diagonals of a parallelogram bisect
each other, and conversely, rectangles are parallelograms with congruent diagonals.
Make geometric constructions
12. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a
segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
Similarity, Right Triangles, and Trigonometry G-SRT
Understand similarity in terms of similarity transformations
1. Verify experimentally the properties of dilations given by a center and a scale
factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel
line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale
factor.
2. Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality of all corresponding pairs of
angles and the proportionality of all corresponding pairs of sides.
3. Use the properties of similarity transformations to establish the AA criterion for
two triangles to be similar.
Prove theorems involving similarity
4. Prove theorems about triangles. Theorems include: a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean
Theorem proved using triangle similarity.
5. Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the
angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
7. Explain and use the relationship between the sine and cosine of complementary
angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
Apply trigonometry to general triangles
9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the opposite side.
10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
11. (+) Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems,
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
resultant forces).
Circles G-C
Understand and apply theorems about circles
1. Prove that all circles are similar.
2. Identify and describe relationships among inscribed angles, radii, and chords.
Include the relationship between central, inscribed, and circumscribed angles;
inscribed angles on a diameter are right angles; the radius of a circle is
perpendicular to the tangent where the radius intersects the circle.
3. Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
5. Derive using similarity the fact that the length of the arc intercepted by an angle is
proportional to the radius, and define the radian measure of the angle as the
constant of proportionality; derive the formula for the area of a sector.
Expressing Geometric Properties with Equations G-GPE
Translate between the geometric description and the equation for a
conic section
1. Derive the equation of a circle of given center and radius using the Pythagorean
Theorem; complete the square to find the center and radius of a circle given by an
equation.
2. Derive the equation of a parabola given a focus and directrix.
3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
Use coordinates to prove simple geometric theorems algebraically
4. Use coordinates to prove simple geometric theorems algebraically. For example,
prove or disprove that a figure defined by four given points in the coordinate plane is
a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the
origin and containing the point (0, 2).
5. Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a
given line that passes through a given point).
6. Find the point on a directed line segment between two given points that partitions
the segment in a given ratio.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
7. Use coordinates to compute perimeters of polygons and areas of triangles and
rectangles, e.g., using the distance formula.
Geometric Measurement and Dimension G-GMD
Explain volume formulas and use them to solve problems
1. Give an informal argument for the formulas for the circumference of a circle, area
of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the
volume of a sphere and other solid figures.
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
Visualize relationships between two-dimensional and three dimensional
objects
4. Identify the shapes of two-dimensional cross-sections of three dimensional
objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
Modeling with Geometry G-MG
Apply geometric concepts in modeling situations
1. Use geometric shapes, their measures, and their properties to describe objects
(e.g., modeling a tree trunk or a human torso as a cylinder).
2. Apply concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost; working with typographic
grid systems based on ratios).
Standards for Mathematical Practice
SMP1. Make sense of problems and persevere in solving them.
SMP2. Reason abstractly and quantitatively.
SMP3. Construct viable arguments and critique the reasoning of others.
SMP4. Model with mathematics.
SMP5. Use appropriate tools strategically.
SMP6. Attend to precision
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
SMP7. Look for and make use of structure.
SMP8. Look for and express regularity in repeated reasoning.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS