Question

What is the reason for statement 3 in this proof?

definition of angle bisector

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Corresponding angles of congruent triangles are congruent.

Done

Given: Δ ABC is an isosceles triangle where AB = BC (view diagram).
Prove: m∠BAC=m∠BCA
Statement Reason
1. Let ΔABC be an isosceles
triangle where AB = BC. given
2. Create point D on side AC¯¯¯¯¯ so
that BD¯¯¯¯¯ bisects ∠ABC as shown. constructing an angle bisector
3. m∠ABD=m∠CBD
4. BD = BD Reflexive Property of Equality
5. ΔABD≅ΔCBD