In δabc shown below, line segment ab is congruent to line segment bc:

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. segment bd ≅ segment bd 3. reflexive property
4. 4. side-angle-side (sas) postulate
5. ∠bac ≅ ∠bca 5. cpctc

which statement can be used to fill in the numbered blank space?

a. δdab ≅ δdbc
b. δabd ≅ δabc
c. δabc ≅ δcbd
d. δabd ≅ δcbd