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

Explanation:

To solve this, we analyze the congruent triangles and their marked corresponding parts.

Step 1: Identify Corresponding Angles

• $\angle A$ (with one arc) corresponds to $\angle Z$ (with one arc).
• $\angle B$ (with one tick mark on sides) corresponds to $\angle Y$ (with one tick mark on sides).
• $\angle C$ (with two arc marks) corresponds to $\angle X$ (with two arc marks).

Step 2: Identify Corresponding Sides

• $\overline{AB}$ (with two tick marks) corresponds to $\overline{ZY}$ (with two tick marks).
• $\overline{AC}$ (with one tick mark) corresponds to $\overline{ZX}$ (with one tick mark).
• $\overline{BC}$ (with two tick marks on the base) corresponds to $\overline{YX}$ (with two tick marks on the top).

Step 3: Triangle Congruence Statement

• For $\triangle CAB$, we match the vertices: $C$ corresponds to $X$, $A$ corresponds to $Z$, $B$ corresponds to $Y$. So $\triangle CAB \cong \triangle XZY$.

Part (a)

• $\angle A \cong \angle Z$
• $\angle B \cong \angle Y$
• $\angle C \cong \angle X$

Part (b)

• $\overline{AB} \cong \overline{ZY}$
• $\overline{AC} \cong \overline{ZX}$
• $\overline{BC} \cong \overline{YX}$

Part (c)

• $\triangle CAB \cong \triangle XZY$

Answer:

s:
(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) $\triangle CAB \cong \triangle XZY$

(For the fill - in - the - blanks in the original problem:
(a) $\angle A \cong \angle \boldsymbol{Z}$, $\angle B \cong \angle \boldsymbol{Y}$, $\angle C \cong \angle \boldsymbol{X}$
(b) $\overline{AB} \cong \overline{\boldsymbol{ZY}}$, $\overline{AC} \cong \overline{\boldsymbol{ZX}}$, $\overline{BC} \cong \overline{\boldsymbol{YX}}$
(c) $\triangle CAB \cong \triangle \boldsymbol{XZY}$)