Lesson plan

Develop an understanding of the properties of the Fundamental Theorem of Similarity by analyzing dilations

teaches Common Core State Standards CCSS.Math.Content.8.G.A.3 http://corestandards.org/Math/Content/8/G/A/3
teaches Common Core State Standards CCSS.Math.Content.8.G.A.4 http://corestandards.org/Math/Content/8/G/A/4
teaches Common Core State Standards CCSS.Math.Content.8.G.A.5 http://corestandards.org/Math/Content/8/G/A/5

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Big Ideas: Triangle similarity exists between a figure and its image if two of their corresponding angles are congruent and/or their corresponding sides are in proportion. When you dilate two points, P and Q from the same center, using the same scale factor, the line segments PQ and P'Q' will be parallel and the length of P'Q' will be r times the length of PQ. This task builds on students' knowledge of dilations, scale factor, and similarity. Students are presented with the task of designing roofs for houses. Students will analyze the designs and the relationships between angles and lines that make up each roof. Students will be asked to generalize in order to figure out the Fundamental Theorem of Similarity, which states that if two points are dilated, P and Q with center O and scale factor r, the lines PQ and P’Q' will be parallel, or |P’Q’|=r|PQ|. Vocabulary: The Fundamental Theorem of Similarity Special Materials: protractor, ruler