Point E is the midpoint of side BC of parallelogram ABCD, and point F is the midpoint of side AD Prove that quadrilateral AFCE i
s a parallelogram.
2 answers:
Answer:
See proof below
Step-by-step explanation:
<u>Theorem:</u> If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.
Consider parallelogram ABCD. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Thus, BC||AD. A parallelogram has 2 sets of opposite sides congruent. Thus, BC=AD.
If E and F are midpoints of sides BC and AD, then halves of these sides are congruent too (CE=FA).
In the quadrilateral AFCE, we have congruent and parallel sides EC and FA. Thus, this quadrilateral is a parallelogram.
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