Question

Given:
AB || DE
C is the midpoint of BD
Prove:
C is the midpoint of AE​

Answer 1

Explanation:

Given: AB║DE and C is the midpoint of BD.

To prove: C is the midpoint of A

Statements Reasons

1). AB║DE 1). Given

2). BC ≅ CD 2). Point C is the midpoint of BD

3). m∠B ≅ m∠D 3). Interior alternate angles

4). m∠ACB ≅ m∠DCE 4). Vertical angles

5). ΔABC ≅ ΔDEC 5). ASA property of congruence

6). AC ≅ EC 6). ΔABC ≅ ΔDEC

7). AC =
`(1)/(2)(\text{AE})` 7). AC ≅ EC