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January 26 2016 Topic A: Dilation • 8th Grade Module 3 Similarity 8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Lessons 1: What Lies Behind the Same Shape? Problem Set Materials Lesson 1 Sample Solutions Lessons 2: Properties of Dilations Problem Set Materials Lesson 2 Sample Solutions Lesson 3: Examples of Dilations Problem Set Materials Video Support Video #1: Explore Dilations Video #2: Identifying Dilations Video #3: Geomtery-Dilations Video #1: Drawing Dilations Video #2: Constructing a Dilation Video #3: Scalar Dilation Construction Sample Solutions Video #1: What is a dilation? Video #2: Drawing Dilations Video #3: Enlarging Shapes Video #4: Dilation and Scale Factor Part 1 (Simplifying Math) Lesson 3 Lesson 4: Fundamental Theorem of Similarity Problem Set Materials Lesson 4 Sample Solutions Lesson 5: First Consequences of FTS Problem Set Materials Lesson 5 Sample Solutions Video #1: Analyze dilation of parallelograms Video #2: How do you find a scale factor in similar figures? Video #1: Understand that a dilation takes a line not passing through the center to a parallel line January 26 2016 Lesson 6: Dilations on the Coordinate Plane Problem Set Materials Lesson 6 Sample Solutions Lesson 7: Informal Proofs of Properties of Dilations Problem Set Materials Lesson 7 Sample Solutions Video #1: Dilation Of Objects On The Coordinate Plane Video #2: Coordinate Rules for Dilations on a Graph Video #1: 8th Grade Dilations and scale factor Topic B: Similar Figures • 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. Lesson 8: Similarity Problem Set Materials Sample Solutions 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 8 Lesson 9: Basic Properties of Similarity Problem Set Materials Lesson 9 Sample Solutions Video #1: Prove two figures are congruent after a series of reflections, rotations or dilations Video #2: The transitive property of Similar Triangles January 26 2016 Lessons 10: Informal Proof of AA Criterion for Similarity Problem Set Materials Lesson 10 Sample Solutions Lesson 11: More About Similar Triangles Problem Set Materials Lesson 11 Sample Solutions Lesson 12: Modeling Using Similarity Problem Set Materials Lesson 12 Sample Solutions Topic C: The Pythagorean Theorem • • 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 Video #1: How do you find missing measurements of similar figures using a scale factor? Video #2: How to solve similar triangle application problems: Flagpole Shadows Video #3: Similar Triangles 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 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three January 26 2016 dimensions. Lesson 13: : Proof of the Pythagorean Theorem Problem Set Materials Lesson 13 Sample Solutions Lesson 14: The Converse of the Pythagorean Theorem Problem Set Materials Lesson 14 Sample Solutions Video #1 What is the Pythagorean Theorem? Video #2: How do you determine if a triangle is a right triangle if you know its sides? Video #3: Pythagorean Theorem proof from similar right triangles Video #1: How do you determine if a triangle is a right triangle if you know its sides? Video #2: Converse of the Pythagorean Theorem Video #3: Converse of the Pythagorean Theorem