8. Elena is proving the Pythagorean Theorem. She knows the goal is to prove
that a² + b² = c² in a right triangle. So far she has: (Lesson 3-14)
X
D
h
C
2002
y
In a right triangle the altitude that intersects the hypotenuse decomposes the
triangle into 2 smaller right triangles. These triangles are similar to the large
triangle by the Angle-Angle Triangle Similarity Theorem since each smaller
triangle shares one angle with the larger triangle and has a right angle. Similar
and
. I can
= xc and b² = yc. Therefore a² + b² = ...
triangles have proportional side lengths, so
rewrite those equations to get a²
Fill in the blanks and finish the proof Elena started.