Question

1. given: \\( \overline{xy} \cong \overline{zw} \\) and \\( \overline{zy} \cong \overline{wx} \\). state which postulate or theorem you can use to prove that the triangles are congruent. how can you use this to prove that \\( \angle y \cong \angle w \\)? a aas; corresponding parts of congruent triangles are congruent. b asa; corresponding parts of congruent triangles are congruent. c sss; corresponding parts of congruent triangles are congruent. d sas; corresponding parts of congruent triangles are congruent. 2. in a right triangle, the sides that are adjacent to the right angle are called the a leg b hypotenuse c right angle d acute angle

Explanation:

Question 1

To determine the congruence postulate, we analyze the given information: $\overline{XY} \cong \overline{ZW}$, $\overline{ZY} \cong \overline{WX}$, and the common side $\overline{XZ} \cong \overline{XZ}$ (reflexive property). This means all three sides of $\triangle XYZ$ and $\triangle ZWX$ are congruent, so we use the SSS (Side - Side - Side) postulate. Once the triangles are congruent by SSS, we can use the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem to show $\angle Y \cong \angle W$.

In a right triangle, the sides adjacent to the right angle are called legs. The hypotenuse is the side opposite the right angle, a right angle is the $90^{\circ}$ angle, and acute angles are the other two angles (less than $90^{\circ}$) in the right triangle.

Answer:

C. SSS; Corresponding parts of congruent triangles are congruent.

Question 2