Chapter 2.8, Problem 11PSB

To determine

To prove that the given angles are congruent.

Answer to Problem 11PSB

  $\angle 1\text{ \& }\angle 2$ are congruent.

Explanation of Solution

Given information :

  $\overleftrightarrow{\text{GD}}\text{ bisects }\angle \text{CBE}$

Formula used:

Congruency means same size and same shape

Vertically opposite angles are equal

Proof:

Since

  $\overleftrightarrow{\text{GD}}\text{ bisects }\angle \text{CBE}$

  $\begin{array}{l}\therefore \angle \text{CBD=}\angle \text{EBD}\\ \Rightarrow \angle \text{3=}\angle \text{2}\mathrm{..............}\left(i\right)\\ \text{From given figure,}\\ \angle 1\text{=}\angle \mathrm{3..........}\left(\text{vertically opposite angles}\right)\\ \angle 1\text{=}\angle \mathrm{2........}\left(\text{from}\left(i\right),\angle \text{3=}\angle \text{2}\right)\\ \text{Thus,}\\ \angle 1\cong \angle \text{2}\end{array}$

Hence, Proved