Chapter 8.4, Problem 11PSA

To determine

To show that two sides are parallel.

Answer to Problem 11PSA

  $\overline{AB}and\overline{DE}areparallel.$

Explanation of Solution

Given information:

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}AC/CE=BC/CD\\ AB/DE=BC/CD\end{array}$

Formula used:

The below properties are used:

Corresponding sides of similar triangles are proportional.

Corresponding angles of similar triangles are congruent.

If alternate interior angles are congruent then the lines are parallel.

Proof:

  

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}AC/CE=BC/CD\\ 6/15=4/10\\ 60=60\end{array}$

  $\begin{array}{l}AB/DE=BC/CD\\ 8/20=4/10\\ 80=80\end{array}$

Corresponding angles of similar triangles are congruent.

  $\therefore \angle A\cong \angle E$

If alternate interior angles are congruent then the lines are parallel.

  $\therefore \overline{AB}and\overline{DE}areparallel.$