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HONORS Geometry Unit 1
Basics of Geometry
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. History
A.1
A.2
A.3
A.4
A.5
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.1
1.2
1.4
1.5
1.7
1.8
1.9
1.10
2.1
2.2
2.3
2.4
2.5
3.1
3.2
4.1
4.2
5.1
5.2
6.1
6.2
B. Review of Coordinate
Geometry
Name 3 historical origins of geometry
Name modern uses of geometry
Name important contributions of Euclid
Name important contributions of Descartes
Name important contributions of Pythagoras
C. Inductive Reasoning
D. Structure of
Mathematical System
B.1 Plot a point
B.2 Identify coordinates of a plotted point
B.3 Calculate distance
B.4 Measure the length of a segment
B.5 Calculate midpoint
B.6 Construct midpoint
B.7 Construct an angle and angle bisector
B.8 Calculate the measure of an angle using angles pairs
(vertical, linear pair, complements, supplements)
B.9 Classify angles (acute, right, obtuse, straight)
B.10 Calculate perimeter and area of basic shapes
(triangles, rectangles, circles)
C.1 Define inductive logic and counterexample
C.2 Formulate a conjecture
C.3 Apply a definition
C.4 Formulate a definition
C.5 Predict a pattern
D.1 Define postulate
D.2 Define theorem
D.3 Define and identify assumption
D.4 Explain and illustrate geometric terms (defined and
undefined)
HONORS Geometry Unit # 2
Logic
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Reasoning
A.1Define and identify a hypothesis
A.2 Define and identify a conclusion
A.3 Identify, write, and analyze conditional statements
A.4 Identify and write converses
A.5 Identify and write negations
A.6 Identify and write inverses
A.7 Identify and write contrapositives
A.8 Identify and write biconditional statements
A.9 Identify equivalent statements
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.1
1.2
1.3
1.4
1.5
1.6
1.8
1.10
2.3
B. Arguments
C. Constructions
D. Truth Tables
B.1 Define and identify logical argument
B.2 Construct a logical argument
B.3 Judge the validity of a logical argument
B.4 Draw conclusions using logical reasoning
B.5 Define and identify deductive reasoning
B.6 Draw conclusions using deductive reasoning with
definitions
B.7 Use symbolic notation to represent an argument
B.8 Apply detachment and syllogism to an argument
B.9 Apply algebraic properties to solve an equation
B.10 Write a two-column proof for equations
B.11 Write a two-column proof for special angles and
segments
B.12 Justify segment an angle congruence using
properties
B.13 Apply postulates to problem solving
C.1 Copy an angle
C.2 Copy a segment
D.1 Apply basic rules of logic using truth tables to
determine the validity of a statement
HONORS Geometry Unit # 3
Parallel and Perpendicular Lines
(3 weeks)
Topic
Geometry
Content
A. Parallel
B. Perpendicular
C. Arguments
D. Slope
Skills
A.1 Define and identify parallel lines and skew lines
A.2 Compare perpendicular, parallel and skew lines
A.3 Compare parallel lines to parallel planes
A.4 Construct parallel lines
A.5 Define and identify a transversal
A.6 Identify special angle pairs formed by parallel lines
and a transversal
A.7 Prove lines are parallel using special angle theorems
A.8 Calculate measures of special angles on parallel
lines
A.9 Create proofs using converses of the parallel
postulate and theorems
A.10 Construct perspective drawings to represent
parallel lines realistically
A.11 Solve real-life problems using parallel lines
A.12 Represent parallel lines in 3-dimensional space
B.1 Define and identify perpendicular lines
B.2 Compare perpendicular lines and skew lines
B.3 Calculate measures of angles formed by
perpendicular lines
B.4 Create proofs using perpendicular theorems
B.5 Construct perpendicular lines
C.1 Create a flow proof
C.2 Create a paragraph proof
C.3 Create a two-coumn proof
D.1 Define and calculate slope
D.2 Identify the y-intercept of a line
D.3 Use slopes to identify parallel and perpendicular
lines
D.4 Write the equation of a line using slope and yintercept, using two points, and from a graph
D.5 Identify an write the equations of parallel and
perpendicular lines
Assessments
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
Standards
1.1
1.2
1.6
1.8
1.9
1.10
2.2
2.3
2.5
HONORS Geometry Unit # 4
Congruent Triangles
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Terminology
A.1 Define triangle and related terms
A.2 Classify triangles by sides
A.3 Classify triangles by angles
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.10
3.4
3.5
3.6
3.7
3.8
3.9
3.10
B. Triangle Relationships
C. Triangle Congruence
D. Special Triangle
Congruences
B.1 Apply triangles inequality
B.2 Find the possible lengths of the third side of a
triangle
B.3 Calculate the third angle of a triangle
B.4 Find interior and exterior angles of a triangle using
the exterior angles theorem
B.5 Find the measures of the angles and sides of a right
triangle
C.1 Indentify and prove triangles are congruent by
corresponding parts
C.2 Apply the Third Angle Theorem
C.3 Explain properties of congruent triangles (Reflexive,
Symmetric, & Transitive)
C.4 Prove triangles are congruent by postulates and
theorems
C.5 Construct congruent triangles using congruence
postulates and theorems
C.6 Complete a coordinate proof of congruent triangles
D.1 Apply Base Angles Theorem and its converse
D.2 Apply equilateral/Equiangular corollary and its
converse
HONORS Geometry Unit # 5
Properties of Triangles
(3 weeks)
Topic
Geometry
Content
Perpendicular Bisectors
B. Angle Bisectors
C. Points of Concurrency
D. Segments of triangles
D.1 Midsegments
D.2 Triangle Inequality
D.3 Hinge Theorem
Skills
A.1 Define and identify a perpendicular bisector
A.2 Calculate angle measures and segment lengths
using a perpendicular bisector
A.3 Complete proofs using perpendicular bisectors
A.4 Construct a perpendicular bisector with straight edge
and compass
B.1 Define and identify an angle bisector
B.2 Calculate angle measures and segment lengths
using angle bisectors
B.3 Complete proofs using angle bisectors
B.4 Construct an angle bisector using straight edge and
compass
E. Indirect Proof
C.1 Identify, locate, and define points of concurrency
C.2 Calculate segment lengths using right triangles and
congruent triangles determined by points of concurrency
C.3 Solve for segment lengths using circles determined
by circumcircle and incircle
C.4 Construct all four points of concurrency with
geometry software
D.1 Construct the midsegment of a triangle
D.2 Calculate segment lengths using the midsegment
theorem
D.3 Complete proofs using the midsegment theorem.
D.4 Calculate side lengths of triangles using the triangle
inequality theorem
D.5 Order the angle measures and side lengths of a
triangle by size
D.6 Compare side lengths and angle measures using the
Hinge theorem and its converse
E.1 Complete an indirect proof
Assessments
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
Standards
1.1
1.4
1.6
1.9
1.10
2.2
2.5
3.5
3.10
6.1
6.2
HONORS Geometry Unit # 6
Quadrilaterals
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Polygons
A.1 Define, name, and identify polygons in terms of
number of sides,
convex/concave, equilateral/equiangular/regular
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.1
1.3
1.10
2.1
2.2
2.3
2.4
2.5
3.2
3.10
4.1
4.2
4.3
4.5
6.1
6.2
B. Parallelograms
C. Other Quadrilaterals
D. Areas
A.2 Calculate the number of degrees in a convex
polygon.
A.3 Calculate the number of diagonals in a convex
polygon.
B.1 List and apply the 5 properties of a parallelogram to
calculate segment lengths and angle measures
B.2 List and apply 6 ways to prove a quadrilateral is a
parallelogram.
C.1 Identify and define special quadrilaterals, including
rectangle, rhombus, square, trapezoid, isosceles
trapezoids and kites.
C.2 Calculate angle measures and segment lengths from
properties of special quadrilaterals
C.3 Prove a quadrilateral is a special type using twocolumn proof and coordinate geometry proof.
C.4 Calculate the areas of special quadrilaterals and
composite figures
HONORS Geometry Unit # 7
Transformations
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Isometry
A.1 Define and identify the terms: transformation,
preimage, image, and corresponding parts
A.2 Identify translations, reflections, rotations and
dilations visually
A.3 Classify transformations as isometry or not
A.4 Apply transformations to tessellations (regular and
Escher)
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.2
1.10
6.3
6.4
6.5
6.6
6.7
6.8
B. Reflection
C. Rotation
D. Translation
E. Composition
B.1 Identify and define reflection, line of reflection,
and lines of symmetry
B.2 Give coordinates of an image under reflection
C.1 Identify and define rotation, center of rotation, angle
of rotation, and rotational symmetry
C.2 Identify a rotation as equivalent to reflections over
two intersecting lines
D.1 Identify and define translations, vector, and
component forms
D.2 Identify a translation as equivalent to reflections over
two parallel lines
D.3 Apply transformations to figures in the coordinate
plane using matrices and using parallelograms
D.4 Compute the magnitude and direction of a resultant
vector using direct measurement on scale drawing, using
the Pythagorean Theorem if perpendicular
E.1 Define composition and glide reflection
E.2 Perform a glide reflection in a coordinate plane
HONORS Geometry Unit # 8
Similarity
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Review ratio, proportion,
& reducing a square root
A.1 Solve ratio and proportions
A.2 Solve real-life problems using ratio and proportion
B. Similar polygons
B.1 Identify and construct similar polygons
B.2 Identify similar triangles using AA~, SSS~, & SAS~
B.3 Use similar polygons to solve real life problems
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.9
1.10
2.6
3.8
3.9
4.6
6.3
6.4
7.4
C. Segments of similar
polygons
D. Dilations
C.1 Calculate segment lengths using proportionality
theorems
C.2 Calculate segment lengths using geometric mean
E. Self-similarity
D.1 Identify and perform dilations using straightedge/compass and using coordinates
D.2 Use scale factor to determine segment lengths of
similar figures
E.1 Identify and define self-similarity
E.2 Perform an iteration of a fractal
E.3 Locate self-similarity in Pascal's triangle and the
Golden Rectangle
HONORS Geometry Unit # 9
Right Triangle & Trigonometry
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Similar Right Triangles
A.1 Solve proportions using similar right triangle created
by the altitude to the hypotenuse
A.2 Find side lengths of right triangles using geometric
mean theorems
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.1
1.2
1.8
1.9
1.10
2.6
3.1
3.6
3.10
3.11
3.12
B. Pythagorean Theorem
C. Special Right Triangles
D. Trigonometry
E. Vectors
B.1 Reduce and rationalize radicals
B.2 Find the missing side of a right triangle using the
Pythagorean Theorem
B.2 Prove the Pythagorean Theorem
B.3 Classify right triangles as acute, right, or obtuse
using the Converse of the Pythagorean Theorem
B.4 Solve real-world problems using the Pythagorean
Theorem
C.1 Find the missing side lengths of a 45-45-90 triangle
C.2 Find the missing side lengths of a 30-60-90 triangle
D.1 Find sine, cosine, and tangent ratios of a right
triangle
D.2 Calculate the acute angle measures from
trigonometric ratios
D.3 Solve real-world problems using trigonometry with
indirect measurement
D.4 Solve right triangles using two sides of a right
triangles
D.5 Solve right triangles using one side and an acute
angle of a right triangle
E.1 Find the magnitude of a vector
E.2 Find the direction of a vector
E.3 Identify equal and parallel vectors
E.4 Add vectors using the parallelogram method
E.5 Calculate the sum of two vectors
HONORS Geometry Unit # 10
Areas of Polygons and Circles
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Angles of Polygons
A.1 Calculate the sum of the measures of a polygon
A.2 Calculate each interior angle of a regular polygon
A.3 Calculate an exterior angle of a regular polygon
A.4 Calculate the number of sides of a polygon
A.5 Calculate the measure of the central angle of a
regular polygon
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.1
1.8
1.9
2.6
2.7
3.1
3.2
3.3
3.4
3.5
3.6
3.8
3.11
3.12
4.1
4.2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
B. Areas of Regular
Polygons
C. Similar Figures
D. Areas of Circles
E. Geometric Probability
F. Networks
B.1 Calculate the area of an equilateral triangle
B.2 Identify and calculate the length of the apothem
B.3 Calculate the area of a regular polygon
C.1 Calculate side lengths, perimeters, and areas of
similar figures
C.2 Compare perimeters and areas of similar figures
using scale factor
D.1 Calculate the perimeter of a circle
D.2 Calculate arc length and central angle measure for a
sector
D.3 Calculate the area of a circle and a sector
E.1 Calculate the areas of composite figures
E.2 Calculate the geometric probability of a composite
figure
F.1 Define basic terms related to networks
F.2 Determine if a network is traversable
F.3 Apply Euler's Formula for networks
HONORS Geometry Unit # 11
Surface Area and Volume
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Euler's Theorem
A.1 Define polyhedron and related terms
A.2 Identify types of polyhedra
A.3 Apply Euler's Theorem to polyhedral
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.9
1.10
2.7
3.1
3.2
3.3
3.4
3.5
3.6
3.10
3.11
3.12
4.1
4.2
4.3
4.4
4.5
4.6
5.1
5.2
7.1
7.2
7.3
7.4
7.5
7.6
B. Surface Areas
C. Volumes
B. Calculate the surface areas of prisms, cylinders,
pyramids, cones, and spheres
D. Similar Solids
E. Drawing
1. Cross sections
2. Isomorphic
3. Orthographic
C. Calculate the volumes of prisms, cylinders, pyramids,
cones, and spheres
D.1 Define similar solids
D.2 Compare and determine ratios of surface areas of
similar solids
D.3 Compare and determine ratios of volumes of similar
solids
E.1 Sketch cross sections of solids
E.2 Sketch isometric views of solids
E.3 Sketch orthographic views of solids
HONORS Geometry Unit # 12
Circles
(3 weeks)
Topic
Geometry
Content
Skills
Assessments
Standards
A. Terminology
A.1 Define terms relating to circles
B. Tangents, Secants, Arcs,
and Chords
B.1 Calculate lengths of tangents, secants, and chords
B.2 Determine the number of degrees in a central angle
B.3 Calculate measures and lengths of arcs
Oral questions
Textbook exercises
Worksheets
Projects
Unit Test (matching,
multiple choice, open
response)
1.2
1.9
1.10
5.1
5.2
5.3
5.4
5.5
5.6
5.7
7.1
7.2
7.3
C. Inscribed Angles
D. Segment Lengths in
Circles
C.1 Calculate the measure of an inscribed angle or an
intercepted arc
C.2 Calculate the measures of the angles of an
inscribed polygon
E. Equations
D.1 Determine lengths of secant segments and tangent
segments
E.1 Write and Identify the equation of a circle