Question

ABCD is a parallelogram. X and Y are the mid points of AB and CD. show that AXCY is a parallelogram.​

Answer 1

Answer:

Given that Abcd is a parallelogram

which implies AB = DC

and DC is parallel to AB

so AX which is a part of AB shud be parallel to YC which is a part of DC

Now,

Since X and Y are the mid pts

AX=XB and DY=YC

So,......AXYC is a parallelogram

Answer 2

Answer:

Given: ABCD is a llgm. and Y and X are the mid points of it.

To Prove: AXCY is a llgm.

Proof:

AB = CD and AB||CD

Then,

AB/2 = CD/2

CY = AX and CY||AX

If opposite sides are equal and parallel, then the quadrilateral is a llgm.

So, we can say that AXCY is a llgm.