Question

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

Answer 1

∆ABD≈∆CBD

is the s statement

Answer 2

D.
`\triangle ABD\cong \triangle CBD`.

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.