Chapter 4.4, Problem 71STP

a.

To determine

Find the congruent triangles using given diagram

Answer to Problem 71STP

The congruent triangles are

  $\Delta AED\cong \Delta CEB$

Explanation of Solution

Given:

The given diagram is

  

Calculation:

In the given diagram, the congruent triangles are

  $\Delta AED\cong \Delta CEB$

  $\begin{array}{l}\angle C\cong \angle A\\ \angle B\cong \angle D\\ \angle E\cong \angle E\end{array}$

b.

To determine

Prove that the triangles are congruent.

Explanation of Solution

Given:

The given diagram is

  

Calculation:

In the given diagram, in triangles $\Delta AED$ and $\Delta CEB$ .

  $\overline{DE}\cong \overline{BE}=x$

Vertical angles are same.

  $\angle AED\cong \angle CEB$

  $\angle ADE\cong \angle CBE$ (given)

Hence from the ASA property $\Delta AED\cong \Delta CEB$ .

c.

To determine

Find the length of the given line segment.

Answer to Problem 71STP

The value of $\overline{EC}=7$ .

Explanation of Solution

Given:

The given diagram is

  

The given line segment is $\overline{EC}$ .

Calculation:

In the given diagram, in triangles $\Delta AED$ and $\Delta CEB$ .

  $\overline{DE}\cong \overline{BE}=x$

Vertical angles are same.

  $\angle AED\cong \angle CEB$

  $\angle ADE\cong \angle CBE$ (given)

From the ASA property $\Delta AED\cong \Delta CEB$ .

The corresponding parts of congruent triangles are congruent.

  $\begin{array}{l}\overline{EC}\cong \overline{EA}\\ \overline{EA}=7\\ \overline{EC}=7\end{array}$

Hence the value of $\overline{EC}=7$ .