RT.2 Use Triangle Similarity Proof of Pythagorean Theorem with Similar Triangles
Name: Teacher: Date: Per: Right Triangles and Trigonometry Learning Targets Practice 3. Construct viable arguments and critique the reasoning of others. G‐MG I can use formulas to find measurements and solve problems.  Use the Pythagorean theorem and its converse to solve problems. G‐SRTb I can prove theorems involving similarity.  G‐MG.1 Use geometric shapes, their measures, and their properties to describe objects.   Prove the Pythagorean Theorem using triangle similarity. Slide 4 What are the dimensions of your rectangle? Sketch it Slide 5 What is true about your 2 triangles? Convince yourself. Convince a friend. Slide 6 Describe an altitude: What is true about your 3 triangles? Convince yourself. Convince a friend. Slide 7 Label the lengths of each Triangle. Geometry by Southwest Washington Common Core Mathematics Consortium is licensed under a Creative Commons Attribution 4.0 International License 10/31/14 Page 1 of 4 RT.2 Use Triangle Similarity Slide 8 Slide 9 Slide 14 Proof of Pythagorean Theorem with Similar Triangles
Label the sides of the right triangle. Make a list of equivalent ratios Write the ratio for your triangle: short sideLarge 
hypotenuseLarge 

short sideSmall 
hypotenuseSmall 
Slide 15 Write the ratio for your triangle: long sideLarge 
hypotenuseLarge 

long sideMedium 
hypotenuseMedium 
Page 2 of 4 RT.2 Use Triangle Similarity Slide 16 Proof of Pythagorean Theorem with Similar Triangles
Let’s prove Pythagorean Theorem Write the ratio for our general triangle: short sideLarge 
hypotenuseLarge 

short sideSmall 
hypotenuseSmall 
Slide 17 Write the ratio for our general triangle: Slide 18 long sideLarge 
hypotenuseLarge 

long sideMedium 
hypotenuseMedium 
Page 3 of 4 RT.2 Use Triangle Similarity Slide 19 Slide 20 Proof of Pythagorean Theorem with Similar Triangles
Did you hit the targets? I understood the proof of the Pythagorean Theorem using triangle similarity. I understood the explanation of the converse of the Pythagorean Theorem. Practice 3: Construct viable arguments and critique the reasoning of others. Exercises: The Pythagorean Theorem and its Converse. Page 4 of 4