Let AABC be any right triangle (see figure below), with the measures of the sides as indicated and the altitude to the hypotenuse of length h. Observe the triangles formed by drawing this altitude, CD, which are separated and rearranged into comparable positions. B Z CL C D b C2 1. How are the three triangles related? How do you know? Original triangle b Subtriangle h #1 C1 Subhange C₂ h 2. Determine all the equivalent ratios between the side lengths for the original triangle and sub-triangle #1. 3. Determine all the equivalent ratios between the side lengths for the original triangle and sub-triangle #2. 4. Use some of the ratios you found in #2 and #3 to derive the Pythagorean Theorem, e.g., a² + b² = c².

Let AABC be any right triangle (see figure below), with the measures of the sides as indicated and the altitude to the hypotenuse of length h. Observe the triangles formed by drawing this altitude, CD, which are separated and rearranged into comparable positions. B Z CL C D b C2 1. How are the three triangles related? How do you know? Original triangle b Subtriangle h #1 C1 Subhange C₂ h 2. Determine all the equivalent ratios between the side lengths for the original triangle and sub-triangle #1. 3. Determine all the equivalent ratios between the side lengths for the original triangle and sub-triangle #2. 4. Use some of the ratios you found in #2 and #3 to derive the Pythagorean Theorem, e.g., a² + b² = c².

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

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