Question

which of the following are congruent? select four correct answers.

□ △stv and △utv
□ overline {st} and overline {tv}
□ ∠stv and ∠svt
□ overline {uv} and overline {sv}
□ ∠u and ∠s
□ ∠tvu and ∠svt

Explanation:

Step1: Check congruent triangles

In \(\triangle STV\) and \(\triangle UTV\):

• \(ST = UT\) (marked with one dash)
• \(SV = UV\) (marked with two dashes)
• \(TV=TV\) (common side)

By SSS (Side - Side - Side) congruence criterion, \(\triangle STV\cong\triangle UTV\)

Step2: Check angles \(\angle U\) and \(\angle S\)

Since \(\triangle STV\cong\triangle UTV\), corresponding parts of congruent triangles are congruent. So \(\angle S=\angle U\) (corresponding angles of \(\triangle STV\) and \(\triangle UTV\))

Step3: Check sides \(\overline{UV}\) and \(\overline{SV}\)

From the markings on the figure, \(SV = UV\) (marked with two dashes)

Step4: Check angles \(\angle TVU\) and \(\angle SVT\)

Since \(\triangle STV\cong\triangle UTV\), \(\angle SVT=\angle TVU\) (corresponding angles)

Answer:

\(\triangle STV\) and \(\triangle UTV\), \(\angle U\) and \(\angle S\), \(\overline{UV}\) and \(\overline{SV}\), \(\angle TVU\) and \(\angle SVT\)