Question

given: \\( \triangle abc \\) is an isosceles triangle where \\( ab = bc \\) prove: \\( m\angle bac = m\angle bca \\) what is the reason for statement 3 in this proof? a. definition of angle bisector b. alternate interior angles theorem c. corresponding angles theorem

Explanation:

Since \(BD\) bisects \(\angle ABC\) (from statement 2), by the definition of an angle bisector, it divides \(\angle ABC\) into two equal - measure angles. So, \(m\angle ABD=m\angle CBD\). The Alternate Interior Angles Theorem is about angles formed by a transversal and parallel lines. The Corresponding Angles Theorem is also about angles formed by a transversal and parallel lines. But here, we are dealing with an angle bisector.

Answer:

A. definition of angle bisector