Question

ABCD is a parallelogram. M is the midpoint of AB and N is the midpoint of CD. Prove that DM parallel to BN.

Answer 1

Answer:

Step-by-step explanation:

In triangles ΔBMC and ΔDME, angle BMC = angle DME; angle BCM = angle MDE ; and DM = MC.  So the two triangles are congruent.

So, BC = DE = AD.          

 AE = 2 AD = 2 BC

In triangles ΔALE and ΔBLC, angle ALE = angle BLC; angle LAE = LCB ; So the triangles are similar.

AB / BC = 2   

  EL / BL = 2     EL = 2 BL