Chapter 2.6, Problem 7CE

To determine

To describe: Plan for proving $\angle 1\cong \angle 4$

Explanation of Solution

Given:

The given figure is,

  ’

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

As given, $\angle 2\cong \angle 3$

So, $m\angle 2=m\angle 3$ ….. (1)

Now, $m\angle 1=m\angle 2$ ….. (2) (Alternate opposite angle)

And, $\text{m}\angle 3=m\angle 4$ ……. (3) (Alternate opposite angle)

From (1) and (3)

  $\text{m}\angle 2=m\angle 4$ ……. (4) (Since both are equal to $m\angle 3$ )

From (2) and (4)

  $\text{m}\angle 1=m\angle 4$ (Since both are equal to $m\angle 2$ )

Hence, $\angle 1\cong \angle 4$