Question

lesson 1: congruent parts, part 1
cool down: making angle bisectors
triangle ( abc ) is a reflection of triangle ( abc ) across line ( bc ). prove that ray ( bc ) is the angle bisector of angle ( aba ).

Explanation:

Step1: Use the property of reflection

Since \(A'B'C'\) is a reflection of \(ABC\) across \(BC\), then \(\triangle ABC\cong\triangle A'B'C'\). So, \(\angle ABC=\angle A'B'C'\).

Step2: Use the fact that \(B = B'\) and \(C = C'\)

Because of the reflection, \(BC\) is the line of reflection. The measure of \(\angle ABC\) and \(\angle A'BC\) (since \(B' = B\) and \(C'=C\)) are equal.

Answer:

Since \(\triangle ABC\cong\triangle A'B'C'\) (by the definition of reflection), \(\angle ABC=\angle A'BC\). By the definition of an angle - bisector (a ray that divides an angle into two equal - measure angles), ray \(BC\) is the angle bisector of \(\angle ABA'\).