Question

Use the image to answer the question.

On right triangle upper A upper B upper C, the altitude of vertex upper C is drawn as a solid line that extends from upper C to the hypotenuse, upper A upper B. The intersection of the altitude and upper A upper B is labeled upper O.

Given is the right triangle ABC
with altitude CO
. Which one of the following statements is true and contributes to the proof of the Pythagorean Theorem?

(1 point)
Responses

△AOC∼△BOC
triangle upper A upper B upper C congruent to triangle upper A upper C upper O

△AOC∼△COB
triangle upper A upper B upper C congruent to triangle upper A upper C upper O

△ABC∼△AOC
triangle upper A upper B upper C congruent to triangle upper A upper C upper O

△ABC∼△BOC
triangle upper A upper B upper C congruent to triangle upper A upper C upper O
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Answer 1

△ABC ∼ △AOC.

Reason: ∠A is common and each triangle is right, so the triangles are similar. From similarity AC/AB = AO/AC so AC^2 = AO·AB. Similarly from △ABC ∼ △BOC we get BC^2 = BO·AB. Adding gives AC^2 + BC^2 = (AO+BO)·AB = AB^2, which is the Pythagorean Theorem.