Question

points M and N are taken on opposite sides AB and CD respectively of parallelogram ABCD such that AN is equal to CM show that AC and MN bisects each other

Answer 1

Answer:

AC and MN bisect each other

Step-by-step explanation:

The diagonals of a parallelogram  is bisect each other.

It is given that,

In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively  such that AM = CN.

Prove that AMCN is a parallelogram.

In a parallelogram  ABCD,

AB || CD, AB= CD

M is point on AB and N is a point on CD

Therefore AM || CD (Since AB || CD)

also AB= CD,

Therefore AMCN is a parallelogram.

AC and MN are the diagonals of the parallelogram  AMCN

Therefore AC and MN bisect each other

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