Question

1. △abc≅△def. find the length of ca, de, ef. find the angle measure of ∠a,∠b,∠c. since △abc≅△def, these six facts are always true. corresponding sides are congruent. corresponding angles are congruent. the side lengths are as follows: ca = 3.5 cm, de = 2.6 cm, ef = 3.7 cm. the angle measures are as follows: m∠a = 73°, m∠b = 65°, m∠c = 42°

Explanation:

Step1: Recall congruent - triangle property

If $\triangle ABC\cong\triangle DEF$, then corresponding sides are equal and corresponding angles are equal.

Step2: Identify corresponding sides

We know that if $\triangle ABC\cong\triangle DEF$, then $\overline{CA}=\overline{FD}$, $\overline{DE}=\overline{AB}$, $\overline{EF}=\overline{BC}$. Given $\overline{CA} = 3.5$ cm, $\overline{DE}=2.6$ cm, $\overline{EF}=3.7$ cm.

Step3: Identify corresponding angles

If $\triangle ABC\cong\triangle DEF$, then $\angle A=\angle D$, $\angle B=\angle E$, $\angle C=\angle F$. Given $\angle D = 73^{\circ}$, $\angle E=65^{\circ}$, $\angle F = 42^{\circ}$, so $m\angle A=73^{\circ}$, $m\angle B = 65^{\circ}$, $m\angle C=42^{\circ}$.

Answer:

$\overline{CA}=3.5$ cm, $\overline{DE}=2.6$ cm, $\overline{EF}=3.7$ cm, $m\angle A = 73^{\circ}$, $m\angle B=65^{\circ}$, $m\angle C = 42^{\circ}$