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Similar Triangles

Similar Triangles. December 16-20, 2013. Big Ideas. Students will write ratios, write and solve proportions, and identify similar polygons using the AA Similarity postulate and the SS and SAS Similarity Theorem. Essential Question. How can two objects be similar?

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Similar Triangles

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  1. Similar Triangles December 16-20, 2013

  2. Big Ideas • Students will write ratios, write and solve proportions, and identify similar polygons using the AA Similarity postulate and the SS and SAS Similarity Theorem.

  3. Essential Question • How can two objects be similar? • How does similarity in mathematics compare to similarity in everyday life?

  4. Standards • CCSS.Math.Content.HSG-MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). • CCSS.Math.Content.HSG-SRT.A.2 : Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. • CCSS.Math.Content.HSG-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. • CCSS.Math.Content.HSG-SRT.B.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figure • CCSS.Math.Content.HSG-GPE.B.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

  5. Understanding • Students can explain the difference between congruence theorems and similarity theorems. • Students can explain how to use proportions to identify similar polygons. • Students can apply their knowledge of proportions to solve real life problems.

  6. Knowledge • Students will recognize and use proportional relationships of corresponding segments of similar triangles.

  7. Skills • Students can write and solve proportions.

  8. Expectations • Hard Work/ High Effort • Ask questions for clarification • Work together to foster learning • Stay on task

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