Question

ru ≅ sv and ∠s ≅ ∠u. complete the proof that △qsv ≅ △qur.

statement
1 ru ≅ sv
2 ∠s ≅ ∠u
3 ∠q ≅ ∠q
4 △qsv ≅ △qur
reason

Explanation:

Step1: Given

The problem states \(RU\cong SV\) and \(\angle S\cong\angle U\). These are given conditions.

Step2: Reflexive property of congruence

For any angle \(\angle Q\), \(\angle Q\cong\angle Q\) by the reflexive property of congruence (an angle is congruent to itself).

Step3: AAS (Angle - Angle - Side) congruence criterion

In \(\triangle QSV\) and \(\triangle QUR\), we have \(\angle S\cong\angle U\) (given), \(\angle Q\cong\angle Q\) (reflexive property), and \(RU\cong SV\) (given). The AAS (Angle - Angle - Side) congruence criterion states that 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:

1. Given
2. Given
3. Reflexive property of congruence
4. AAS (Angle - Angle - Side) congruence criterion