Question

In ΔABC shown below, Line segment AB is congruent to Line segment BC:

Answer 1

Answer:

D.$\triangle ABD\cong \triangle CBD$.

Step-by-step explanation:

Given

In triangle ABC a line segment AB is congruent to line segment BC.

Given: $\overline{ AB} \cong \overline{BC}$

To prove that the base angles of an isosceles triangle are congruent.

i.e $\angle BAC\cong \angle BCA$

1.Statement: Segment BD is an angle bisector of $\angle ABC$

Reason: By construction.

2.Statement: $\angle ABD\cong \angle CBD$

Reason: By definition of an angle bisector.

3.Statement: $\overline{BD}\cong \overline{BD}$

Reason: Reflexive property .

4. Statement: $\triangle ABD\cong \traingle CBD$

Reason: Side-Angle-Side(SAS)

Postulate

5.Statement:$\angle BAC\cong \angle BCA$

Reason: CPCT.

Hence proved.

Answer 2

∆ABD≈∆CBD

is the s statement