Question

Given is the right triangle
with altitude
. Which one of the following statements is true andcontributes to the proof of the Pythagorean Theorem?
(1 point)
ABC CO
△ABC ∼ △AOC
△ABC ∼ △BOC
△AOC ∼ △COB
△AOC ∼ △BOC

Answer 1

△ABC ∼ △AOC.

Reason: ΔABC and ΔAOC are both right and share angle A, so by AA they are similar. From that similarity AB/AC = AC/AO, so AC^2 = AB·AO. (Similarly from ΔABC ∼ ΔBOC you get BC^2 = AB·BO; adding gives AC^2+BC^2 = AB^2, the Pythagorean theorem.)