Question

and ∠def are congruent. (1)-(5) 4 points each (6)(7) 5 points each c and ∠def (points in order.) (ans.) side de = side (ans.) side fd = side (ans.) ∠acb = ∠ (7) find the measure of ∠def. (ans.)

Explanation:

Step1: Recall congruent - triangle properties

If two triangles are congruent, corresponding sides and angles are equal.

Step2: Identify corresponding sides

For congruent triangles $\triangle ABC$ and $\triangle DEF$, side $DE$ corresponds to side $AB$.

Step3: Identify other corresponding sides

Side $FD$ corresponds to side $CB$.

Step4: Identify corresponding angles

$\angle ACB$ corresponds to $\angle DFE$.

Step5: Find $\angle DEF$ measure

In $\triangle ABC$, $\angle A = 45^{\circ}$ and $\angle C=90^{\circ}$, so $\angle B=180^{\circ}-45^{\circ}-90^{\circ} = 45^{\circ}$. Since $\triangle ABC\cong\triangle DEF$, $\angle DEF=\angle ABC = 45^{\circ}$.

Answer:

side $DE$ = side $AB$
side $FD$ = side $CB$
$\angle ACB=\angle DFE$
$\angle DEF = 45^{\circ}$