Question

BCEADGiven: E is the midpoint of AC and AC bisects BDProve: ADEAZABECWhat theorems/definitions are needed to get the 3 pieces of information on each triangle?Then select the theorem that will prove the triangles are congruent.Vertical angles are congruentDefinition of midpointO Alternate interior angles are congruent

Answer 1

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.