Chapter 6, Problem 15CT

To determine

To prove: angles C and D are not right angles.

Explanation of Solution

Given:

The trapezoid is shown below:

  

The line AB is parallel to DC.

Calculation:

Assume that angles C and D are right angles.

Hence:

  $\angle C=\angle D=90°$

The line AB is parallel to DC.

Hence,

  $\begin{array}{c}\angle A+\angle D=180°\\ \angle A+90°=180°\\ \angle A=90°\end{array}$

And,

  $\begin{array}{c}\angle B+\angle C=180°\\ \angle B+90°=180°\\ \angle B=90°\end{array}$

This shows that all the angles of the trapezoid are right angles which is not possible. This will make ABCD as rectangle, not a trapezoid.

Thus, the assumption is wrong.

Hence, this proves thatanglesC and D are not right angles.