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)

Answer 1

To prove that triangle XZY is congruent to triangle ZXP, we can use the Side-Angle-Side (SAS) congruence theorem.

1. Side XY is congruent to side XZ: This is given because XYZP is a rhombus, and a rhombus has all sides congruent.

2. Side ZY is congruent to side XP: This is also given because XYZP is a rhombus, and a rhombus has all sides congruent.

3. Angle ZXY is congruent to angle ZXO: These angles are opposite each other and are formed by the intersection of the diagonals of the rhombus. Opposite angles in a rhombus are always congruent.

Using the SAS congruence theorem, we have two pairs of congruent sides and one pair of congruent angles. Therefore, triangle XZY is congruent to triangle ZXP.