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) (5 points) Responses They cannot be proven congruent as there is not enough information. They cannot be proven congruent as there is not enough information. SSA - Because the two outsides are equal and angle Z is congruent to angle X because the diagonals bisect the angles. SSA - Because the two outsides are equal and angle Z is congruent to angle X because the diagonals bisect the angles. SSS - Since all sides of a rhombus are equal and XZ is congruent because of the reflexive property. SSS - Since all sides of a rhombus are equal and XZ is congruent because of the reflexive property. AAA - All angles of the triangles are equal therefore the triangles are congruent.

Question

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) (5 points) Responses They cannot be proven congruent as there is not enough information. They cannot be proven congruent as there is not enough information. SSA - Because the two outsides are equal and angle Z is congruent to angle X because the diagonals bisect the angles. SSA - Because the two outsides are equal and angle Z is congruent to angle X because the diagonals bisect the angles. SSS - Since all sides of a rhombus are equal and XZ is congruent because of the reflexive property. SSS - Since all sides of a rhombus are equal and XZ is congruent because of the reflexive property. AAA - All angles of the triangles are equal therefore the triangles are congruent.

Answer 1

The correct answer is SSS - Since all sides of a rhombus are equal and XZ is congruent because of the reflexive property.

To prove that triangle XZY is congruent to triangle ZXP, we need to show that all corresponding sides and angles are congruent.

1. Side XZ is congruent to itself by the reflexive property of congruence.
2. Side ZY is congruent to side ZP because both are sides of the rhombus XYZP, and all sides of a rhombus are equal.
3. Side XY is congruent to side XP because both are diagonals of the rhombus XYZP, and the diagonals of a rhombus bisect each other.

Therefore, we have shown that all three sides of triangle XZY are congruent to the corresponding sides of triangle ZXP, satisfying the condition for SSS (Side-Side-Side) congruence.