Chapter E, Problem 3.4EX

To determine

To find of the following would allow you to conclude that $\overline{AD}\parallel \overline{BC}$ .

Answer to Problem 3.4EX

Option (a) $\angle DEC\cong \angle BEC$ is correct.

Explanation of Solution

Given information: Figure,

Options,

a. $\angle DEC\cong \angle BEC$

b. $\angle ABE\cong \angle BEC$

c. $\angle BEC\cong \angle BCE$

d. $m\angle A+m\angle AEC=180$

Calculation: The required solutions is obtained as,

If two parallel lines are by cut by a transversal, then alternate interior angles are congruent.

  $\begin{array}{l}AD\parallel BC\\ m\angle DEC=m\angle BCE\end{array}$

Therefore, option (a) $\angle DEC\cong \angle BEC$ is correct.