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) $\triangle acbcong\trianglesquare$

Explanation:

Step1: Identify corresponding angles

When two triangles are congruent, angles with the same number of arc - markings are corresponding. So, $\angle A\cong\angle X$, $\angle B\cong\angle Z$, $\angle C\cong\angle Y$.

Step2: Identify corresponding sides

Sides with the same number of tick - markings are corresponding. So, $\overline{AB}\cong\overline{XZ}$, $\overline{AC}\cong\overline{XY}$, $\overline{BC}\cong\overline{ZY}$.

Step3: Write the congruence statement

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

Answer:

(a) $\angle A\cong\angle X$, $\angle B\cong\angle Z$, $\angle C\cong\angle Y$
(b) $\overline{AB}\cong\overline{XZ}$, $\overline{AC}\cong\overline{XY}$, $\overline{BC}\cong\overline{ZY}$
(c) $\triangle ACB\cong\triangle XYZ$