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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∼△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

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

△ABC∼△AOC

Answer 1

To prove the Pythagorean Theorem using the right triangle \( ABC \) and its altitude \( CO \), we can examine the similarity of triangles formed by this altitude.

The correct statement that contributes to the proof of the Pythagorean Theorem is:

△AOC ∼ △BOC

This statement indicates that triangles \( AOC \) and \( BOC \) are similar. This similarity allows us to set up proportions involving the lengths of the sides, which is essential in proving the relationships between the sides of triangle \( ABC \) and the segments formed by the altitude \( CO \) on the hypotenuse \( AB \).

Thus, the response would be:

△AOC ∼ △BOC