Question

given: △uxw and △uvw are right △s.
ux ≅ uv
prove: ∠x ≅ ∠v
(there is a diagram of the triangles and a table with statements and reasons:

1. △uxw and △uvw are right △s. 1.
2. ux ≅ uv 2.
3. uw ≅ uw 3.
4. c. △uxw ≅ △uvw 4.
5. ∠x ≅ ∠v 5. )

Explanation:

Step1: Identify Given Info

1. Given: $\triangle UXW$ and $\triangle UVW$ are right $\triangle$s (Reason: Given).
2. Given: $\overline{UX} \cong \overline{UV}$ (Reason: Given).
3. $\overline{UW} \cong \overline{UW}$ (Reason: Reflexive Property of Congruence).

Step2: Prove Triangles Congruent

1. $\triangle UXW \cong \triangle UVW$ (Reason: HL (Hypotenuse-Leg) Congruence Theorem, since both are right triangles, hypotenuse $\overline{UX} \cong \overline{UV}$ and leg $\overline{UW}$ is common).

Step3: Corresponding Parts Congruent

1. $\angle X \cong \angle V$ (Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC)).

Answer:

1. Reason: Given
2. Reason: Given
3. Reason: Reflexive Property of Congruence
4. Reason: HL Congruence Theorem
5. Reason: CPCTC