Question

Triangle ABC is a reflection of ABC across line BC. Prove that ray BC is the triangle bisector of angle ABA.

a. Prove that BC is perpendicular to AA′.
b. Prove that ABA≅ABC.
c. Prove that BC bisects angle ABA.
d. Prove that AA ′ ≅AA'.

Answer 1

To prove that ray BC is the triangle bisector of angle ABA, we need to show that AB is congruent to BC and angle A is congruent to angle C. We can use the fact that a reflection preserves angles and distances to prove these properties.

Step-by-step explanation:

To prove that ray BC is the triangle bisector of angle ABA, we need to show that AB is congruent to BC and angle A is congruent to angle C.

a. To prove that BC is perpendicular to AA', we can use the fact that the reflection of a line is perpendicular to the line it reflects across. Since triangle ABC is a reflection of ABC across line BC, BC is perpendicular to AA'.

b. To prove that ABA is congruent to ABC, we can use the fact that a reflection preserves angles. Since triangle ABC is a reflection of ABC, angle ABA is congruent to angle BCB.

c. To prove that BC bisects angle ABA, we need to show that angle A and angle C are congruent. Since triangle ABC is a reflection of ABC, angle A is congruent to angle C.

d. To prove that AA' is congruent to AA', we can use the fact that a reflection preserves distances. Since triangle ABC is a reflection of ABC, AA' is congruent to AA'.