Question

1. given: \\( \overline { p q } \cong \overline { s r } \\), \\( \angle p q r \cong \angle s r q \\) prove: \\( \triangle p q r \cong \triangle s r q \\)

Explanation:

Step1: Identify the given information

• Given: $\overline{PQ}\cong\overline{SR}$, $\angle PQR\cong\angle SRQ$
• Also, $\overline{QR}\cong\overline{RQ}$ (common side, reflexive property of congruence)

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

• In $\triangle PQR$ and $\triangle SRQ$:
• We have $\overline{PQ}\cong\overline{SR}$ (given side)
• $\angle PQR\cong\angle SRQ$ (given angle)
• $\overline{QR}\cong\overline{RQ}$ (common side)

Answer:

Statements	Reasons
2. $\angle PQR\cong\angle SRQ$	2. Given
3. $\overline{QR}\cong\overline{RQ}$	3. Reflexive property of congruence
4. $\triangle PQR\cong\triangle SRQ$	4. SAS (Side - Angle - Side) congruence criterion