Question

Name

8.2 Using Parallelograms in Proofs
1. Given: Parallelogram ABCD
DE I AB
BFI DC
с
Prove: DE 2 BF
A
E
B

Answer 1

Explanation:

1) Parallelogram ABCD,
`\overline{DE} \perp \overline{AB}, \overline{BF} \perp \overline{DC}` (given)

2)
`\angle DAE \cong \angle FCB` (opposite angles of a parallelogram are congruent)

3)
`\angle AED` and
`\angle BFC` are right angles (perpendicular lines form right angles)

4)
`\angle AED \cong \angle BFC` (all right angles are congruent)

5)
`\overline{AD} \cong \overline{BC}` (opposite sides of a parallelogram are congruent)

6)
`\triangle AED \cong \triangle CFB` (AAS)

7)
`\overline{DE} \cong \overline{BF}` (CPCTC)