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Math Question

\( Y Q \) and \( \overline{X P} \) are altitudes to the congruent sides of isosceles triangle \( \triangle W X Y \). Keisha is going to prove \( \overline{Y Q} \cong \overline{X P} \) by showing they are congruent parts of the congruent triangles \( \triangle Q X Y \) and \( \triangle P Y X \). By what congruence postulate is \( \triangle Q X Y \cong \triangle P Y X \) ? None of the other answers are correct SSA - because segment \( \overline{X Y} \) is shared; segments \( \overline{X P} \) and \( \overline{Y Q} \) are altitudes, and \( W X Y \) is isosceles, so base angles are congruent. SSS - because segment \( \overline{Q P} \) would be parallel to segment \( \overline{X Y} \). ASA - because triangle \( W X Y \) is isosceles, its base angles are congruent. Segment \( \overline{X Y} \) is shared; and perpendicular lines form right angles, which are congruent. AAS - because triangle \( W X Y \) is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment \( \overline{X Y} \) is shared.

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