We are given that ACDH is a parallelogram and asked to show that when we cut it in half, ABFH will also be a parallelogram.
Let's focus on sides AB and HF.
By definition, the opposite sides of parallelogram ACDH are parallel, so AB and HF are parallel.
AB∥HF
Theorem 6.3 tells us that the opposite sides of parallelogram ACDH are congruent. Since B and F are midpoints of segments AC and HD, this means that AB and HF are half of congruent segments, so they themselves are congruent.
AB≅HF
Since sides AB and HF are both parallel and congruent, Theorem 6.12 tells us that quadrilateral ABFH is a parallelogram. We can summarize this process in a flow proof.
Completed Proof
2
&Given:&& ACDH is a parallelogram
& && Bis the midpoint ofAC
& && Fis the midpoint ofHD
&Prove:&& ABFH is a parallelogram
Proof:
