Question

Point E is the midpoint of side BC of parallelogram ABCD, and point F is the midpoint of side AD. prove that quadrilateral BEDF is a parallelogram

Answer 1

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Step-by-step explanation:

Here is one way to go about it.

Statement . . . . Reason

1. AD ≅ BC, AD║BC, E & F are midpoints of BC, AD . . . . given

2. (1/2)AD ≅ (1/2)BC . . . . multiplicative property of congruence (equality)

3. DF = (1/2)AD, BE = (1/2)BC . . . . definition of midpoint

4. DF ≅ BE . . . . substitution property of congruence

5. BE║DF . . . . segments of parallel lines are parallel

6. BEDF is a parallelogram . . . . BE ≅ DF, BE║DF, definition of parallelogram