Question

e 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) $\angle a \cong \angle \square$ $\angle b \cong \angle \square$ $\angle c \cong \angle \square$ (b) $\overline{ab} \cong \overline{\square}$ $\overline{ac} \cong \overline{\square}$ $\overline{bc} \cong \overline{\square}$ (c) $\triangle cba \cong \triangle \square$

Explanation:

Step1: Match congruent angles

Look at marked angles:
$\angle A$ (3 marks) $\cong \angle Z$ (3 marks)
$\angle B$ (2 marks) $\cong \angle Y$ (2 marks)
$\angle C$ (1 mark) $\cong \angle X$ (1 mark)

Step2: Match congruent sides

Look at marked sides:
$\overline{AB}$ (3 marks) $\cong \overline{YZ}$ (3 marks)
$\overline{AC}$ (2 marks) $\cong \overline{ZX}$ (2 marks)
$\overline{BC}$ (1 mark) $\cong \overline{XY}$ (1 mark)

Step3: Write congruence statement

Map vertices: $C \to X$, $B \to Y$, $A \to Z$, so $\triangle CBA \cong \triangle XYZ$

Answer:

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