Chapter 4.4, Problem 17WE

To determine

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

Explanation of Solution

Given:

The given figure is,

  

And the condition is,

  $\overline{XY}\cong \overline{XZ}\text{and }\overline{OY}\cong \overline{OZ}$

Statement :	Reason:
$\overline{XY}\cong \overline{XZ}$ and $\overline{OY}\cong \overline{OZ}$	Given
$m\angle 2=m\angle 3$	Isosceles triangle property (for $\Delta OYZ$)
$m\angle 1+m\angle 2=m\angle 3+m\angle 4$	Isosceles triangle property (for $\Delta XYZ$)
$m\angle 1=m\angle 4$	Since, $m\angle 2=m\angle 3$ so cancels out
$m\angle 1=m\angle 4$	Proved