Question

which postulate proves the two triangles congruent?
asa congruence postulate
sss congruence postulate
segment congruence postulate
sas congruence postulate

Explanation:

Step1: Analyze the given markings

The markings show that \(QS = QR\), \(PS = PR\), and \(QP = QP\) (common side).

Step2: Recall congruence postulates

• ASA (Angle - Side - Angle): Requires two angles and the included side.
• SSS (Side - Side - Side): Requires three sides.
• Segment Congruence Postulate: Not a triangle congruence postulate.
• SAS (Side - Angle - Side): Requires two sides and the included angle.

Since we have three pairs of equal sides (\(QS = QR\), \(PS = PR\), \(QP = QP\)), the SSS Congruence Postulate applies.

Answer:

SSS Congruence Postulate