Chapter 2.6, Problem 19WE

To determine

To prove: $\angle 1\cong \angle 4$ using two column method.

Explanation of Solution

Given:

The given figure is,

  ’

And the condition is, $\angle 2\cong \angle 3$

Steps:	Reason:
$\angle 2\cong \angle 3$	Given
$m\angle 2=m\angle 3$	Congruent angles are equal
$m\angle 1=m\angle 2$	Alternate opposite angle
$\text{m}\angle 3=m\angle 4$	Alternate opposite angle
$\text{m}\angle 1=m\angle 4$	Since, $m\angle 1=m\angle 2$, $\text{m}\angle 3=m\angle 4$ and $m\angle 2=m\angle 3$
$\angle 1\cong \angle 4$	Since, equal angles are congruent