Question

18. YQ and XP are altitudes to the congruent sides of Isosceles triangle WXY. Keisha is going to prove that YQ S XP, by showing that they are congruent parts of congruent triangles QXY and PYX . tto A. AAS, because AWXY is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment XY is shared. B. SSS, because segment QP would be parallel to XY. C. SSA, because segment XY would be shared; segments XP and YQ are altitudes, and AWXY is isosceles, so base angles are congruent. D. ASA, because AWXY is isosceles, its base angles are congruent. Segment XY is shared; perpendicular lines form right angles, which are congruent.

Answer 1

Consider the given figure.

It is required to prove that traingles PYX and QXY are congruent.

Both the triangles share a common base XY.

The lines PX and QY are perpendicular on congruent sides, so PX must be equal to QY.

According to the theorem "Angles opposite to equal sides are equal", it follows that anglea PYX and QXY are equal.

Thus, it is observed that the two triangles PYX and QXY have 2 sides and one angle equal. Therefore, the two triangles will be congruent on the basis of SSA criteria.

Therefore, option C is the correct choice.