Question

1. if △cfg≅△ytr, complete each congruence statement using corresponding parts

\\(\overline{cg}\cong\\)
\\(\overline{fc}\cong\\)
\\(\angle cgf\cong\\)
\\(\triangle gcf\cong\\)
drag and drop the correct choice into the blank spaces above
\\(\triangle yrt\\) \\(\triangle rty\\) \\(\overline{yt}\\) \\(\triangle ytr\\) \\(\triangle ryt\\) \\(\angle ryt\\)
\\(\triangle tyr\\) \\(\overline{rt}\\) \\(\angle ytr\\) \\(\triangle try\\) \\(\overline{yr}\\) \\(\angle try\\)

Explanation:

Step1: Recall congruent - triangle property

When $\triangle CFG\cong\triangle YTR$, corresponding sides and angles are congruent.

Step2: Find $\overline{CG}$'s corresponding side

The corresponding side of $\overline{CG}$ is $\overline{YR}$, so $\overline{CG}\cong\overline{YR}$.

Step3: Find $\overline{FC}$'s corresponding side

The corresponding side of $\overline{FC}$ is $\overline{TY}$, but there is no $\overline{TY}$ in the options. Since $\overline{FC}$ and $\overline{YT}$ are the same line - segment just named in reverse order, $\overline{FC}\cong\overline{YT}$.

Step4: Find $\angle CGF$'s corresponding angle

The corresponding angle of $\angle CGF$ is $\angle RYT$, so $\angle CGF\cong\angle RYT$.

Step5: Find $\triangle GCF$'s corresponding triangle

The corresponding triangle of $\triangle GCF$ is $\triangle RTY$, so $\triangle GCF\cong\triangle RTY$.

Answer:

$\overline{CG}\cong\overline{YR}$
$\overline{FC}\cong\overline{YT}$
$\angle CGF\cong\angle RYT$
$\triangle GCF\cong\triangle RTY$