Question

∠u ≅ ∠v and (overline{uv} perp overline{tw}). complete the proof that ( \triangle tvw cong \triangle tuw ).

Explanation:

Step1: Analyze the reason for $\overline{TW}\cong\overline{TW}$

Any segment is congruent to itself. This is the reflexive property of congruence.

Step2: Determine the congruence criterion for $\triangle TVW\cong\triangle TUW$

We have $\angle U\cong\angle V$ (given), $\angle TWU\cong\angle TWV$ (all right angles are congruent), and $\overline{TW}\cong\overline{TW}$ (reflexive property). By the AAS (Angle - Angle - Side) congruence criterion, if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

For statement 4, the reason is "Reflexive property of congruence". For statement 5, the reason is "AAS (Angle - Angle - Side)".