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.
First, we can establish that side XZ is congruent to side ZX, as both are two sides of the same rhombus XYZP and all sides of a rhombus are congruent.
Next, we know that angle XZY is congruent to angle ZXP. This is because opposite angles in a rhombus are congruent. In the rhombus XYZP, angle XZY is opposite to angle ZXP, thus they are congruent.
Finally, we can conclude that side XY is congruent to side ZP. This is because all sides of a rhombus are congruent, and side XY is congruent to side ZP as they are opposite sides in the rhombus XYZP.
Therefore, triangle XZY is congruent to triangle ZXP by the SAS congruence theorem, with the congruent sides being XZ and ZP, and the congruent angle being angle XZY/angle ZXP.