Question

1. given: sr || tu and ∠s ≅ ∠u

prove: △srt ≅ △utr
statement

1. given
2. sr || tu

3.
4.
5.
reason
1.
2.
3.
4.
5.

Explanation:

Step1: Alternate interior angles

Since \(SR\parallel TU\), by the property of parallel lines, \(\angle SRT=\angle UTR\) (alternate - interior angles).

Step2: Reflexive property

\(RT = TR\) (reflexive property of equality, a segment is equal to itself).

Step3: ASA (Angle - Side - Angle) criterion

We are given \(\angle S=\angle U\), from step1 \(\angle SRT=\angle UTR\), and from step2 \(RT = TR\). So, by the ASA (Angle - Side - Angle) congruence criterion, \(\triangle SRT\cong\triangle UTR\).

Answer:

1. Given; 2. \(\angle SRT=\angle UTR\), \(SR\parallel TU\) (alternate - interior angles); 3. \(RT = TR\), reflexive property; 4. \(\angle S=\angle U\), given; 5. \(\triangle SRT\cong\triangle UTR\), ASA