In ΔABC shown below, line segment AB is congruent to line segment BC:
Triangle ABC, where sides AB and CB are congruent
Given: line segment AB≅line segment BC
Prove: The base angles of an isosceles triangle are congruent.
The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent:
Statement Reason
1. segment BD is an angle bisector of ∠ABC. 1. by Construction
2. 2. Definition of an Angle Bisector
3. segment BD ≅ segment BD 3. Reflexive Property
4. ΔABD ≅ ΔCBD 4. Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA 5. CPCTC
Which statement can be used to fill in the numbered blank space?
∠DBA ≅ ∠CDB
∠CAB ≅ ∠ACB
∠ABD ≅ ∠CBD
∠BDA ≅ ∠BDC