the triangles below are congruent and their corresponding parts are marked. name all the corresponding…

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) $\triangle baccong\trianglesquare$

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) $\triangle baccong\trianglesquare$

Answer

Explanation:

Step1: Identify corresponding angles

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

Step2: Identify corresponding sides

Based on the congruence - marking, we match the sides. $\overline{AB}\cong\overline{ZY}$, $\overline{AC}\cong\overline{ZX}$, $\overline{BC}\cong\overline{YX}$

Step3: Write the triangle - congruence statement

The order of vertices in the congruence statement matters. Since $\angle B$ corresponds to $\angle Y$, $\angle A$ corresponds to $\angle Z$, and $\angle C$ corresponds to $\angle X$, we have $\triangle BAC\cong\triangle YZX$

Answer:

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