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.
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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∼△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

△AOC∼△BOC

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: ∠C is right in △ABC and ∠COA is right in △AOC, and they share ∠A, so the triangles are similar. From that similarity you get b^2 = c·AO (and similarly from △ABC ∼ △BOC you get a^2 = c·BO), and adding those gives a^2 + b^2 = c^2 (the Pythagorean theorem).