Question

Solve the following Proof.

Given: Ray BD bisects angle ABC
Prove: Measure of angle ABD is equal to 1/2 measure of angle ABC.

Answer 1

The proof is completed by utilizing the definition of an angle bisector to establish that the measure of angle ABD is equal to measure of angle DBC, and then employing algebra to show measure of angle ABD is half of measure of angle ABC.

Step-by-step explanation:

To solve a geometry proof where it is given that ray BD bisects angle ABC, and we need to prove that the measure of angle ABD is equal to 1/2 measure of angle ABC, we proceed as follows:

1. By definition of an angle bisector, it divides the angle into two equal parts. Therefore, the measure of angle ABD is equal to the measure of angle DBC.
2. Since ray BD is the bisector of angle ABC, we can say: measure of angle ABD + measure of angle DBC = measure of angle ABC.
3. Substituting the equal measures from step 1 into step 2, we have: 2 * measure of angle ABD = measure of angle ABC.
4. Dividing both sides by 2, we get the measure of angle ABD = 1/2 measure of angle ABC, which is what we were asked to prove.