Problem

1. $\triangle A B C \cong \boldsymbol{D E F}$. Find the length of $C \overline{A, D E, E F}$. Find the angle measure of $\angle A, \angle B, \angle C$.
Since $\triangle A B C \cong \triangle D E F$, these six facts are always true.
Corresponding sides are congruent $\quad$ Corresponding angles are congruent
The side lengths are as follows:
The angle measures are as follows:
\[
\begin{array}{l}
C A=3.5 \mathrm{~cm} \\
-D E=2.6 \mathrm{~cm} \\
E F=3.7 \mathrm{~cm}
\end{array}
\]
\[
\begin{array}{l}
m \angle A=73^{\circ} \\
m \angle B=65^{\circ} \\
m \angle C=42^{\circ}
\end{array}
\]

Answer

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Answer

So, the length of $\overline{CAD}$ is \(\boxed{3.5}\) cm and the measures of $\angle A$, $\angle B$, and $\angle C$ are \(\boxed{73^\circ}\), \(\boxed{65^\circ}\), and \(\boxed{42^\circ}\) respectively.

Steps

Step 1 :Since the triangles $\triangle ABC$ and $\triangle DEF$ are congruent, their corresponding sides and angles are equal.

Step 2 :Therefore, the length of $\overline{CAD}$ is equal to the length of $\overline{CA}$, which is 3.5 cm.

Step 3 :Similarly, the measures of $\angle A$, $\angle B$, and $\angle C$ are equal to the measures of $\angle D$, $\angle E$, and $\angle F$ respectively, which are $73^\circ$, $65^\circ$, and $42^\circ$.

Step 4 :So, the length of $\overline{CAD}$ is \(\boxed{3.5}\) cm and the measures of $\angle A$, $\angle B$, and $\angle C$ are \(\boxed{73^\circ}\), \(\boxed{65^\circ}\), and \(\boxed{42^\circ}\) respectively.

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