Question

use the given information to prove that ∠srt ≅ ∠urt.

given: ( overline{st} cong overline{ut} )
( overline{rs} cong overline{ru} )
prove: ( angle srt cong angle urt )

Explanation:

Step1: Write the given information

Given \( \overline{ST}\cong\overline{UT}\), \( \overline{RS}\cong\overline{RU}\), and \( \overline{RT}\cong\overline{RT}\) (common side).

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

In \(\triangle SRT\) and \(\triangle URT\),

$$
LATEXBLOCK0
$$

So, \(\triangle SRT\cong\triangle URT\) (by SSS).

Step3: Use CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since \(\triangle SRT\cong\triangle URT\), then \( \angle SRT\cong\angle URT\) (CPCTC).

Answer:

\(\angle SRT\cong\angle URT\) is proved as above.