Chapter 12.4, Problem 38E

(a)

To determine

To Explain: Why $\Delta ABE\cong \Delta DCE$ .

Answer to Problem 38E

Because it follow the side-angle-side congruency rule.

Explanation of Solution

Given:

  

In $\Delta ABEand\Delta DCE$

  $\begin{array}{l}\overline{AB}\cong \overline{DC}\\ \overline{AE}\cong \overline{DE}\\ \angle BAE\cong \angle CDE\\ thus\\ BySASrule\\ \Delta ABE\cong \Delta DCE\end{array}$

(b)

To determine

To Find: The name of isosceles triangle in the purse.

Answer to Problem 38E

  $\Delta BCEand\Delta ADE$

Explanation of Solution

Given:

  

  $\begin{array}{l}\Delta BCE\left(\overline{BE}\cong \overline{CE}\right)\\ \Delta ADE\left(\overline{AE}\cong \overline{DE}\right)\end{array}$

(c)

To determine

To Find: The name of three angles that are congruent to $\angle EAD.$

Answer to Problem 38E

  $\angle ADE,\angle EBCand\angle ECB.$

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle AED\cong \angle BEC={100}^{°}\\ \angle EAD=\angle EDA=\frac{180-100}{2}={40}^{°}\\ \angle EBC=\angle ECB=\frac{180-100}{2}={40}^{°}\end{array}$

Thus

The three angles that are congruent to $\angle EAD$ are $\angle ADE,\angle EBCand\angle ECB.$