Triangle Angle Bisector Proof

Question

Given: Triangle ABD is an equilateral triangle and E is the midpoint of segment AD.

 

Prove: Segment EB bisects angle DBA.

 

Prove: Segment EB is perpendicular to Segment AD

Please also include the reasons in the roof

Answer 1

Statements                                              Reasons

1. ΔABD is an equilateral triangle          1. Given

2. AB ≅ BD                                               2. Definition of an equilateral triangle

3. ∠A ≅ ∠D                                                3. Definition of an equilateral triangle

4. E is the midpoint of AD                       4. Given

5. AE ≅ ED                                                5. Definition of a midpoint

6. ΔABE ≅ ΔDBE                                       6. SAS

7. ∠ABE ≅ ∠DBE                                        7. CPCTC

8. ∴ EB bisects  ∠DBA                               8. Definition of an angle bisector

QED