Question

if $\triangle catcong\triangle dog$, 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
b. is $angle acongangle d$ necessarily true?
a. yes. since the triangles are congruent and $angle a$ corresponds to $angle d$, $angle acongangle d$
b. no. $angle a$ and $angle d$ are not corresponding angles in the triangles

Explanation:

When two triangles are congruent, corresponding parts (sides and angles) are congruent. For part a, $\overline{CT}$ and $\overline{DG}$ are corresponding sides of congruent triangles $\triangle CAT$ and $\triangle DOG$, so $\overline{CT}\cong\overline{DG}$. For part b, $\angle A$ and $\angle D$ are corresponding angles of congruent triangles $\triangle CAT$ and $\triangle DOG$, so $\angle A\cong\angle D$.

Answer:

a. A. Yes. Since the triangles are congruent and $\overline{CT}$ corresponds to $\overline{DG}$, $\overline{CT}\cong\overline{DG}$
b. A. Yes. Since the triangles are congruent and $\angle A$ corresponds to $\angle D$, $\angle A\cong\angle D$