XYZP is a rhombus. Explain why triangle XZY is congruent to triangle ZXP. ( Hint: You must prove the triangle congruent with a triangle congruence theorem and explain the criteria required including naming the congruent sides/ angles)
Triangle XZY is congruent to triangle ZXP because of the Side-Angle-Side (SAS) congruence theorem. This theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and angle of another triangle, then the triangles are congruent.
In this case, we can see that:
1. Side XZ is congruent to side XZ (common side).
2. Side ZY is congruent to side XP (opposite sides of a rhombus are congruent).
To complete the SAS congruence, we need to demonstrate that the included angles are congruent. The included angle for triangle XZY is angle Z and the included angle for triangle ZXP is angle X.
Since XYZP is a rhombus, its opposite angles are congruent. Therefore, we can conclude that angle Z is congruent to angle X.
By satisfying the SAS congruence criteria, we can state that triangle XZY is congruent to triangle ZXP.