Question

∠v ≅ ∠w. complete the proof that \overline{uw} ≅ \overline{uv}.

1 ∠v ≅ ∠w given
2 \overline{vw} ≅ \overline{vw}
3 \triangle uvw ≅ \triangle uwv
4 \overline{uw} ≅ \overline{uv}

Explanation:

Step1: Reflexive property of congruence

$$\overline{VW}\cong\overline{VW}$$

Step2: ASA (Angle - Side - Angle) Congruence

Since $\angle V\cong\angle W$, $\overline{VW}\cong\overline{VW}$ and $\angle VWU=\angle WVU$ (common angle), by ASA congruence criterion $\triangle UVW\cong\triangle UWV$

Step3: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

If $\triangle UVW\cong\triangle UWV$, then $\overline{UW}\cong\overline{UV}$

Answer:

1. Reflexive property of congruence; 3. ASA Congruence; 4. CPCTC