Chapter 9.3, Problem 81E

Proof of the Pythagorean Theorem by Similar Triangles In the figure, right triangles ABC. CBD, and ACD are similar. This may be used to prove the Pythagorean theorem. Fill in the blanks with the appropriate responses.

(a) By proportion, we have $\frac{c}{b}=\_\_\_/j$.

(b) By proportion, we also have $\frac{c}{a}=a/\_\_\_\_$.

(c) Form part (a), $b^2=\_\_\_\_$.

(d) Form part (b), $a^2=\_\_\_\_$.

(e) Form the result of parts (c) and (d) and factoring $a^2+b^2=c$

(____ ) Since ____ $=c$, it follows that ____.