A prove Keisha can use to show congruent parts of congruent triangles QXY and PYX is: A. AAS, because ΔWXY is isosceles, its base angles are congruent. Perpendicular lines form right angles, which are congruent; and segment XY is shared.
In Mathematics and Euclidean Geometry, AAS is an abbreviation for Angle-Angle-Side and it states that when two (2) angles and the non-included side (adjacent to only one of the angles) in two triangles are all equal, then the triangles are said to be congruent.
Based on the angle, angle, side (AAS) congruence theorem, we can logically deduce that triangle QXY and triangle PYX are both congruent based on the following statements;
YQ = XP
∠WXY = ∠WYX
WQ/QX = WP/PY
PQ ║ XY
∠PXY = ∠QYX
The SSS congruence theorem cannot be used because we can't tell if sides XQ and PY or sides QY and PX are congruent. SSA is not a valid congruence theorem, so it cannot be used.
Since we can't tell if angles QYX and PXY are congruent, the ASA congruence theorem cannot be used.