Question

What is the reason for statement 5 in this proof?

ASA

SSS

AAS

SAS
Done
Given: ΔABC, where AB = BC (view diagram)
Prove: m∠BAC=m∠BCA

Statement
Reason
1. Let ΔABC be an isosceles triangle with
AB = BC.

given

2. Create point D on side AC¯¯¯¯¯ so BD¯¯¯¯¯ bisects
∠ABC.

constructing an angle bisector

3. m∠ABD=m∠CBD

definition of angle bisector

4. BD = BD

Reflexive Property of Equality

5. ΔABD≅ΔCBD



6. m∠BAC=m∠BCA

Corresponding angles of congruent triangles have equal measures.