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February 2015 8th Grade 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 • 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: Flagpole Shadows 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: Flagpole Shadows