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```February 2015
Module 5: Geometry
Topic A: Definitions and Properties of the Basic Rigid Motions
•
8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
Why Move Things Around & Translations and Basic Properties
Problem Set
Materials
Sample Solutions
Video Support
Video 1: Rotations, Reflections, and Translations
Video 2: Investigating Translation Effects
Focus B: Translations and Three Basic Properties
Video 1: Translation of the Plane Along a Vector
Video 2: Drawing Translations
Video 3: Translation Vector
Translations of lines & Definition of Reflection Properties
Problem Set
Materials
Definition of Rotation and Basic Properties
Materials
Problem Set
Sample Solutions
Video 1: Drawing Translations
Video 2: Investigating Translation Effects
Focus B: Definition of Reflection and Basic Properties
Video 1: Investigate Reflection Effects
Video 2: Identifying Reflections
Video 3: Drawing Reflections
Video 4: Reflections Concept
Sample Solutions
Video 1: Investigating Rotation Effects
February 2015
Video 2: Identifying Rotations
Video 3: Drawing Rotations
Video 4: Rotating Shapes (stop at 5:17)
Rotation of 180 Degrees
Problem Set
Materials
Sample Solutions
Video 1: Investigating Rotation Effects
Video 2: Drawing Rotations in the Coordinate Plane
Video 3: Rotate 180 Degrees About Origin
Video 4: How Reflections and Rotations
Change Coordinates
Topic B: Sequencing the Basic Rigid Motions
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8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a
sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence
between them.
Sequencing Transformations & Rigid Motions
Problem Set
Materials
Sample Solutions
Video 1: Demonstrate Congruence Using
Transformation
Video 2: Drawing Compositions of Isometries
Transformations & Rigid Motions
Problem Set
Materials
Sample Solutions
Sequencing Transformations & Rigid Motions
Problem Set
Materials
Sample Solutions
Video 1: Composition of Rigid Motions
Video 2: Geometry Transformation
Video 3: Motion Geometry Rotations, Reflections, and
Translations (start at 4:22)
February 2015
Video 1: Composition of Rigid Motions
Video 2: Rotations, Reflections, and Translations
Video 3: Rotate a Point Using Angle Measures and Distances
Sequencing Transformations & Rigid Motions
Video 1: Composition of Rigid Motions
Video 2: Demonstrate Congruence Using Transformation
Video 3: Art Application
Topic C: Congruence and Angle Relationships
•
•
8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of
rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when
parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the
same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Congruence and Angles Associated with Parallel Lines
Problem Set
Materials
Sample Solutions
Video 1: Apply Properties of Congruence to Rotations
Video 2: Apply Properties of Congruence to Reflections
Video 3: Demonstrate Congruence Using Transformation
Focus B: Angles Associated with Parallel Lines
Video 1: What is a Transversal?
Video 2: Relate Angles and Transversals
Video 3: What Are Vertical Angles?
Angle Sum of Triangles
Problem Set
Materials
Sample Solutions
Focus A: Angle Sum of a Triangle
Video 1: What is the Triangle Sum Theorem?
February 2015
Video 2: Find a Missing Angle in a Right Triangle
Video 3: What Are Supplementary Angles?
Video 4: The Interior Angles of Right Triangles
Video 5: Acute, Obtuse, Right, and Straight Angles
Video 6: Equilateral, Isosceles, and Scalene Triangles
Focus B: Angles Associated with Parallel Lines
Video 1: Interior and Exterior Angles
Video 2: The Relationship Between Exterior Angles
Topic A: Dilation
•
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Lesson 1: What Lies Behind the Same Shape?
Problem Set
Materials
Sample Solutions
Lesson 2: Properties of Dilations
Problem Set
Materials
Sample Solutions
Focus A: What Lies Behind “Same Shape”?
Video #1: Explore Dilations
Video #2: Identifying Dilations
Video #3: Geometry-Dilations
Focus A: Properties of Dilations
Video #1: Drawing Dilations
Video #2: Constructing a Dilation
Video #3: Scalar Dilation Construction (Stop at 3:05)
Lesson 3: Examples of Dilations
Problem Set
Materials
Lesson 4: Fundamental Theorem of Similarity
Sample Solutions
Focus A: Examples of Dilations
Video #1: What is a dilation?
Video #2: Drawing Dilations
Video #3: Enlarging Shapes
Video #4: Dilation and Scale Factor Part 1 (Simplifying Math)
February 2015
Problem Set
Materials
Sample Solutions
Focus A: Fundamental Theorem of Similarity
Video #1: Analyze dilation of parallelograms
Video #2: How do you find a scale factor in similar figures?
Lesson 5: First Consequences of FTS
Focus A: First Consequences of Similarity (FTS)
Video #1: Understand that a dilation takes a line not passing
through the center to a parallel line
Lesson 6: Dilations on the Coordinate Plane
Focus A: Dilations on the Coordinate Plane
Video #1: Dilation Of Objects On The Coordinate Plane
Video #2: Coordinate Rules for Dilations on a Graph
Lesson 7: Informal Proofs of Properties of Dilations
Topic B: Similar Figures
•
•
Focus A: Informal Proofs of Properties of Dilations
Video #1: 8th Grade Dilations and scale factor
8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of
rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the
similarity between them.
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when
parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the
same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
February 2015
Lesson 8: Similarity
Problem Set
Materials
Sample Solutions
Focus A: Similarity
Video #1: Drawing Compositions of Isometries
Video #2: Determine if two figures are similar using
transformations and dilations
Video #3: Describe a sequence of transformations
Lesson 9: Basic Properties of Similarity
Problem Set
Materials
Sample Solutions
Focus A: Basic Properties of Similarity
Video #1: Prove two figures are congruent after a series of
reflections, rotations or dilations
Video #2: The transitive property of Similar Triangles
Lesson 10: Informal Proof of AA Criterion for Similarity
Problem Set
Materials
Sample Solutions
Focus A: Informal Proof of AA Criterion for Similarity
Video #1: Determine triangle similarity by checking for
corresponding congruent angles
Video #2: Show triangle similarity using translation
Video #3: Establish triangle similarity using translation and
dilation
Video #4: Understand why the third angles of similar triangles
are congruent
Video #5: Similar triangles using Angle-Angle
Video #6: Prove AA similarity by overlapping angles
Lesson 11: More About Similar Triangles
Problem Set
Materials
Sample Solutions
Focus A: More About Similar Triangles
Video #1: How do you find missing measurements of similar
figures using a scale factor?
February 2015
Video #2: How to solve similar triangle application problems:
Video #3: Similar Triangles
Lesson 12: Modeling Using Similarity
Problem Set
Materials
Sample Solutions
Focus A: Modeling Using Similarity
Video #1: Application of similar triangles: part 1
Video #2: Application of similar triangles: part 2
Video #3: Application of similar triangles: part 3
Video #4: Application of similar triangles: part 4
Video #5: Application of similar triangles: part 5
Video #6: Application of similar triangles: part 6
Video #7: How to solve similar triangle application problems: