Question

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

Answer 1

ΔABD ≅ ΔCBD

Explanation:

Guys this is the right answer, ΔABD ≅ ΔCBD. I got it right on my test!

Answer 2

In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct option for missing statement is D. ΔABD ≅ ΔCBD .