Question

use the given information to prove that $\triangle rsu\cong\triangle tus$. given: $rs = tu$ $ru = ts$ prove: $\triangle rsu\cong\triangle tus$

Explanation:

Step1: List the given information

We are given \(RS = TU\) and \(RU = TS\). Also, in \(\triangle RSU\) and \(\triangle TUS\), \(SU=US\) (common side).

Step2: Apply SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
For \(\triangle RSU\) and \(\triangle TUS\), we have:

• \(RS = TU\) (given)
• \(RU = TS\) (given)
• \(SU = US\) (common side)

Answer:

By the SSS (Side - Side - Side) congruence criterion, \(\triangle RSU\cong\triangle TUS\)