# Thread: parallelogram-how to prove

1. ## parallelogram-how to prove

Given: ABCD - parallelogram
BE=DM
How to prove:
a)ED=MB
b)BEDM-parallelogram ?

2. ## Re: parallelogram-how to prove

Originally Posted by nataku

Given: ABCD - parallelogram
BE=DM
How to prove:
a)ED=MB
b)BEDM-parallelogram ?
You can show that EA and CM are equal. You know BC and AD are equal and that A=C. That gets you BMC and EAD being congruent and thus BM=ED.

There's a proof that if one pair of opposite sides of a quadrilateral is both parallel (BE and MD are parallel because ABCD is a parallelogram) and congruent, (just proved), that the quadrilateral is a parallelogram here at the bottom of the page.

3. ## Re: parallelogram-how to prove

Originally Posted by nataku

Given: ABCD - parallelogram
BE=DM
How to prove:
a)ED=MB b)BEDM-parallelogram ?
You might just notice that $m(BE)=m(MD)~\&~BE\|MD$ (two parallel sides of equal length).

4. ## Re: parallelogram-how to prove

Originally Posted by romsek
You can show that EA and CM are equal. You know BC and AD are equal and that A=C. That gets you BMC and EAD being congruent and thus BM=ED.

There's a proof that if one pair of opposite sides of a quadrilateral is both parallel (BE and MD are parallel because ABCD is a parallelogram) and congruent, (just proved), that the quadrilateral is a parallelogram here at the bottom of the page.
If both pairs of opposite sides of a quad are congruent then the quad is a parrelogram