Question

the triangles below are congruent and their corresponding parts are marked. name all the corresponding congruent angles and sides. then, complete the triangle congruence statement. (a) $angle aconganglesquare$ (b) $overline{ab}congoverline{square}$ $angle bconganglesquare$ $overline{ac}congoverline{square}$ $angle cconganglesquare$ $overline{bc}congoverline{square}$ (c) $\triangle cbacong\trianglesquare$

Explanation:

Step1: Identify corresponding angles

By the congruence of triangles and the marked - parts, we match the angles.
$\angle A\cong\angle Y$, $\angle B\cong\angle X$, $\angle C\cong\angle Z$

Step2: Identify corresponding sides

We match the sides based on the congruence.
$\overline{AB}\cong\overline{YX}$, $\overline{AC}\cong\overline{YZ}$, $\overline{BC}\cong\overline{ZX}$

Step3: Write the triangle - congruence statement

The order of vertices matters. Since $\angle C$ corresponds to $\angle Z$, $\angle B$ corresponds to $\angle X$, and $\angle A$ corresponds to $\angle Y$, $\triangle CBA\cong\triangle ZXY$

Answer:

(a) $\angle A\cong\angle Y$, $\angle B\cong\angle X$, $\angle C\cong\angle Z$
(b) $\overline{AB}\cong\overline{YX}$, $\overline{AC}\cong\overline{YZ}$, $\overline{BC}\cong\overline{ZX}$
(c) $\triangle CBA\cong\triangle ZXY$