In the triangle above, does \(a^2 + b^2 = c^2 ?\)

[Vincen]

In the triangle above, does \(a^2 + b^2 = c^2 ?\)

(1) \(x + y = 90\)
(2) \(x = y\)

[spoiler]OA=A[/spoiler]

Source: Official Guide

[Scott@TargetTestPrep]

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In the triangle above, does \(a^2 + b^2 = c^2 ?\)

(1) \(x + y = 90\)
(2) \(x = y\)

[spoiler]OA=A[/spoiler]

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine whether a^2 + b^2 = c^2. That is, we need to determine whether the triangle is a right triangle.

Statement One Alone:

Since x + y = 90, the unlabeled angle must be 180 - 90 = 90 degrees. In other words, it’s a right angle, and so the triangle is a right triangle. Therefore, we do have a^2 + b^2 = c^2. Statement one alone is sufficient.

Statement Two Alone:

Statement two is not sufficient. For example, if x = y = 45, then the triangle is a right triangle. However, if x = y ≠ 45, then the triangle is not a right triangle.

Answer: A