1.

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

Answer»

Consider △ AMO and △ CNO

We know that AB || CD

From the figure we know that ∠ MAO and ∠ NCO are alternate angles

It is given that AM = CN

We know that ∠ AOM and ∠ CON are vertically opposite angles

∠ AOM = ∠ CON

By ASA congruence criterion

△ AMO ≅ △ CNO

So we get

AO = CO and MO = NO (c. p. c. t)

Therefore, it is proved that AC and MN bisect each other.


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