Chapter 2, Problem 19CR

To determine

To prove: that $\angle 3\cong \angle 4$

Explanation of Solution

Given information:

Given:

  $\angle 3$ is a supplement of $\angle 1$ ;

  $\angle 4$ is a supplement of $\angle 2$ .

Given figure,

  

Calculation:

Consider the figure

  

Consider the following.

  $\angle 1$ and $\angle 3$ and $\angle 2$ and $\angle 4$ are supplementary

To prove that $\angle 3\cong \angle 4$

Since $\angle 1$ and $\angle 3$ and $\angle 2$ and $\angle 4$ are supplementary

Therefore,

  $\begin{array}{l}\angle 1+\angle 3=180°\\ \angle 2+\angle 4=180°\end{array}$

Also, $\angle 1=\angle 2$ both are vertically opposite angle.

Therefore,

  $\begin{array}{l}\angle 1+\angle 3=180°\\ \angle 1+\angle 4=180°\end{array}$

Therefore, $\angle 3=\angle 4$

Hence, proved.