Question

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. 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?



ΔDAB ≅ ΔDBC


ΔABD ≅ ΔABC


ΔABC ≅ ΔCBD


ΔABD ≅ ΔCBD

Answer 1

Given : ΔABC Line segment AB is congruent to Line segment BC

To Find : Show that The base angles of an isosceles triangle are congruent.

Solution:

line segment AB ≅ line segment BC   given

Statement                                                          

1. segment BD is an angle bisector of ∠ABC.

Reason

1. by Construction

Statement          

2. ∠ABD ≅ ∠CBD          

Reason                

2. Definition of an Angle Bisector

Statement          

3. segment BD ≅ segment BD          

Reason    

3. Reflexive Property

Statement          

4.  ΔABD ≅ ΔCBD      

Reason                      

4. Side-Angle-Side (SAS) Postulate

Statement          

5. ∠BAC ≅ ∠BCA                          

Reason

5. CPCTC

QED Hence proved that Base angles are congruent.

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