Question

if △cat ≅ △dog, determine which of parts (a) through (c), if any, are necessarily true. explain why.
a. is $overline{ct}congoverline{dg}$ necessarily true?
a. yes. since the triangles are congruent and $overline{ct}$ corresponds to $overline{dg}$, $overline{ct}congoverline{dg}$.
b. no. $overline{ct}$ and $overline{dg}$ are not corresponding line segments in the two triangles.

Explanation:

Congruent triangles have corresponding parts congruent. In \(\triangle CAT\cong\triangle DOG\), the order of the vertices indicates the correspondence. C corresponds to D, A corresponds to O, and T corresponds to G. So, \(\overline{CT}\) and \(\overline{DG}\) are corresponding line - segments. Since the triangles are congruent, corresponding line - segments are congruent.

Answer:

A. Yes. Since the triangles are congruent and \(\overline{CT}\) corresponds to \(\overline{DG}\), \(\overline{CT}\cong\overline{DG}\)