# ABCD is a parallelogram and X,Y are the mid points of sides AB and DC respectively . show that quadrlaterals AXCY is a parallelogram

given: ABCD is a llgm.

X & Y are the mid points of sides AB & DC respectively.

to prove: quadrilateral AXCY is a llgm.

proof: In AXCY,

AX = CY (AB = CD, X & Y are mid points)

AX ll CY (AB ll CD)

AXCY is a llgm. (if a pair of opp. sides of a quadrilateral are equal and parallel, then it is a llgm)

hope this helps!!!!!!!

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given: ABCD is a llgm.

X & Y are the mid points of sides AB & DC respectively.

to prove: quadrilateral AXCY is a llgm.

proof: In AXCY,

AX = CY (AB = CD, X & Y are mid points)

AX ll CY (AB ll CD)

AXCY is a llgm. (if a pair of opp. sides of a quadrilateral are equal and parallel, then it is a llgm)

hope this helps!!!!!!!

• 8

given: ABCD is a llgm.

X & Y are the mid points of sides AB & DC respectively.

to prove: quadrilateral AXCY is a llgm.

proof: In AXCY,

AX = CY (AB = CD, X & Y are mid points)

AX ll CY (AB ll CD)

AXCY is a llgm. (if a pair of opp. sides of a quadrilateral are equal and parallel, then it is a llgm)

hope this helps!!!!!!!

• 6
To prove : AXCY is a IIgm.

Given : (i)ABCD is a IIgm.
(ii) X and Y are the mid points of AB and DC respectively.

Proof : AB II DC ( ABCD is a IIgm)
therefore AX II YC. .............(1)

AB = DC (ABCD is a IIgm)
therefore. 1/2 AB = 1/2 DC
AX = YC. ............(2)

from equation (1) & (2)
AXCY is a IIgm.
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Super jacob
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