In the following diagram acedb, ac = bd and e is the midpoint of cd. explain or prove why it must
also be the midpoint of ab.

1)

Statement Reason
1. ∠1 and ∠3 are vertical angles. 1. Given
2. ∠1 and ∠2 form a linear pair. VAT
∠2 and ∠3 form a linear pair. 2. Definition of linear pair
3. ∠1 and ∠2 are supplementary. Substitution Property
∠2 and ∠3 are supplementary. SAME SIDE INTERIOR ANGLES THEOREM
3. VERTICAL ANGLES THEOREM
4. m∠1 + m∠2 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM
  m∠2 + m∠3 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM
5. m∠1 + m∠2 = m∠2 + m∠3 
(SUBSTITUTION PROPERTY)
6. m∠1 = m∠3 opposite angles
7. ∠1 ≅ ∠3 7. Given