Question

in exercises 1 - 6, decide whether it is possible to prove that the triangles are congruent. if it is possible, state the theorem or postulate you would use. explain your reasoning. (lessons 4.3 and 4.4)
6.

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. So, \(\angle RTS\cong\angle VTU\) (vertical angles theorem).

Step2: Check given congruent parts

We are given \(RS = VU\) (marked on the sides) and \(\angle R=\angle V\) (marked as angles).

Step3: Apply AAS congruence

By the Angle - Angle - Side (AAS) congruence theorem, 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 triangles are congruent. Here, \(\angle R=\angle V\), \(\angle RTS=\angle VTU\), and \(RS = VU\).

Answer:

It is possible to prove the triangles congruent. We use the AAS (Angle - Angle - Side) congruence theorem.