Chapter 2, Problem 26RP

To determine

To show that two angles are congruent.

Explanation of Solution

Given information: $\overline{BC}bisects\angle DBE.$

Formula used: The below properties are used:

If a ray bisects an angle, it divides the angle into two congruent angles.

If the sum of two angles forms a straight line, the angles are supplementary.

Proof: $\overline{BC}bisects\angle DBE.$

  

If a ray bisects an angle, it divides the angle into two congruent angles.

It can be assumed from diagram that ∠ABC to be a straight line.

If the sum of two angles forms a straight line, the angles are supplementary.

∴∠CBD is supplementary to ∠ABD.

Similarly, ∠CBE is supplementary to ∠ABE.

Supplementary of congruent angles are congruent.

  $\angle ABD \cong \angle ABE$