Question

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

Answer 1

It is ABD = CBD I just got it right!

Explanation:

Answer 2

∠ABD ≅ ∠CBD

Explanation:

Given: line segment AB ≅ line segment BC

Prove: The base angles of an isosceles triangle are congruent.

Statement Reason

1. Segment BD is an angle bisector of ∠ABC - By construction

2. ∠ABD ≅ ∠CBD - Definition of an Angle Bisector

3. Segment BD ≅ segment BD - Reflexive Property

4. ΔABD ≅ ΔCBD - Side-Angle-Side (SAS) Postulate

5. ∠BAC ≅ ∠BCA - CPCTC