Chapter 8.5, Problem 28PSC

To determine

To show two sides are parallel.

Explanation of Solution

Given information:

  $\frac{AD}{DB}=\frac{AE}{EC}$

Formula used:

The below properties are used:

Corresponding sides of similar triangles are congruent.

Corresponding angles are congruent if the lines are parallel.

Calculation:

  

It is given that,

  $\frac{AD}{DB}=\frac{AE}{EC}$

By reflexive property, we get

  $\angle A\cong \angle A$

Two triangles are similar by SAS similarity rule.

  $\Delta ADE~\Delta ABC$

Corresponding sides of similar triangles are congruent.

  $\angle ADE\cong \angle ABC$

Corresponding angles are congruent if the lines are parallel.

  $\overline{DE}$ is parallel to $\overline{BC}$ .