Question

tu || vw and ∠w ≅ ∠u. complete the proof that △tuv ≅ △vwt.
statement
1 tu || vw
2 ∠w ≅ ∠u
3 ∠uvt ≅ ∠vwt
4 tv ≅ tv
5 △tuv ≅ △vwt
reason
given
given

reflexive property of congruence

Explanation:

Step1: Identify the reason for ∠UTV ≅ ∠WVU

Since \( TU\parallel VW\), by the Alternate Interior Angles Theorem, \( \angle UTV\cong\angle WVU\).

Step2: Use the AAS (Angle - Angle - Side) Congruence Criterion

We have \( \angle W\cong\angle U\) (given), \( \angle UTV\cong\angle WVU\) (Alternate Interior Angles Theorem), and \( TV = VT\) (Reflexive Property of Congruence). So, by the AAS (Angle - Angle - Side) Congruence Criterion, \( \triangle TUV\cong\triangle VWT\).

Answer:

1. Alternate Interior Angles Theorem; 5. AAS (Angle - Angle - Side) Congruence Criterion