Question

quiz: triangle congruence by sss

1. what additional information do you need to prove △abc≅△def?

(overline{bc}congoverline{ef})
(overline{ab}congoverline{de})
(overline{ac}congoverline{df})

Explanation:

Step1: Recall SSS congruence criterion

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In \(\triangle ABC\) and \(\triangle DEF\), we already know some side - congruence relationships from the markings. We need to complete the set for SSS.

Step2: Analyze given markings

From the figure, we can see some side - congruence markings. We need to find the remaining side - congruence to prove \(\triangle ABC\cong\triangle DEF\) by SSS. If \(\overline{AB}\cong\overline{DE}\), \(\overline{BC}\cong\overline{EF}\), then we need \(\overline{AC}\cong\overline{DF}\) to satisfy the SSS congruence criterion.

Answer:

\(\overline{AC}\cong\overline{DF}\)