Chapter 6, Problem 11CUR

To determine

To prove: AECF is a rectangle.

Explanation of Solution

Given:

The quadrilateral is shown below:

  

A line AB is parallel to DC.CE and AF are normal to line AB.

Calculation:

CE and AF are normal to line AB.

Hence,

  $\angle FAE=\angle CEA=90°$

A line AB is parallel to DC. Hence, a line FC must be parallel to AE.

Hence,

  $\begin{array}{c}\angle FAE+\angle AFC=180°\\ \angle AFC+90°=180°\\ \angle AFC=90°\end{array}$

And,

  $\begin{array}{c}\angle CEA+\angle ECF=180°\\ \angle ECF+90°=180°\\ \angle ECF=90°\end{array}$

This shows that all the angles of quadrilateral are right angle. This will make AECF as rectangle.

Hence, this proves thatAECF is a rectangle.