Chapter 2.6, Problem 4CE

To determine

To find: If two angles, $\angle 6$ and $\angle 7$ , are congruent.

Answer to Problem 4CE

Angle bisector theorem states that ”If a line bisects an angle, the angles formed are congruent to each other.”. Thus, it proves that $\angle 6=\angle 7$ .

Explanation of Solution

Given information: In below figure, $\overrightarrow{XZ}$ bisects $\angle WXY$ .

Theorem used: Angle bisector theorem states that ”If a line bisects an angle, the angles formed are congruent to each other.”.

Calculation: As $\overrightarrow{XZ}$ bisects $\angle WXY$ , so,

  $\begin{array}{l}m\angle 6=\frac{1}{2}\angle WXY\mathrm{......}(i)\\ m\angle 7=\frac{1}{2}\angle WXY\mathrm{......}(ii)\end{array}$

Thus, by (i) and (ii),

  $\angle 6=\angle 7$

Conclusion: Thus, using the theorem of angle bisector theorem, it proves that two angles shown are congruent to each other.