Statements → Proof
1. E is the midpoint of AC. → Given
2. AE ≅ EC → Definition of Midpoint
Midpoint is a point that divides a line segment into two equal parts.
3. AC bisects BD → Given
4. BE ≅ ED → Definition of Segment Bisector
A segment bisector is a segment that cuts another line segment into two equal parts.
5. ∠BEC ≅ ∠DEA → Vertical angles are congruent.
5. ∆DEA ≅ ∆BEC → SAS Theorem
Hence, to prove ∆DEA ≅ ∆BEC, we need the following theorems/definition:
a. Definition of Midpoint
b. Definition of Segment Bisector
c. Vertical angles are congruent.
Lastly, the theorem that will prove that the triangles are congruent is SAS Theorem.
