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

3. 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?

line segment BD ≅ line segment AC

line segment BD ≅ line segment BD

line segment AC ≅ line segment AC

line segment AD ≅ line segment DC