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

△ABC∼△AOC

Answer 1

△ABC ∼ △AOC.

Reason: ∠C and ∠O are right and ∠A is common, so by AA the triangles are similar. From the similarity AC/AB = AO/AC so AC^2 = AB·AO. (Similarly △ABC ∼ △BOC gives BC^2 = AB·OB.) Adding AC^2 + BC^2 = AB(AO+OB) = AB^2, which is the Pythagorean theorem.