Question

1. write three valid congruency statements given the triangles below.

Explanation:

Step1: Identify congruence criteria

We use Side - Angle - Side (SAS), Angle - Side - Angle (ASA) and Angle - Angle - Side (AAS) criteria.

Step2: SAS congruence statement

$\triangle PQR\cong\triangle TUS$ (by SAS since two pairs of sides and the included angle are equal as marked).

Step3: ASA congruence statement

$\triangle RQP\cong\triangle UTS$ (by ASA as two pairs of angles and the included side are equal).

Step4: AAS congruence statement

$\triangle QRP\cong\triangle TSU$ (by AAS with two pairs of angles and a non - included side equal).

Answer:

a) $\triangle PQR\cong\triangle TUS$
b) $\triangle RQP\cong\triangle UTS$
c) $\triangle QRP\cong\triangle TSU$