Properties of a Parallelogram

Theorem 1: When we divide a parallelogram into two parts diagonally then it divides it into two congruent triangles.

\mathrm{\triangle ABD\cong CDB}

Theorem 2: In a parallelogram, opposite sides will always be equal.

Theorem 3: A quadrilateral will be a parallelogram if each pair of its opposite sides will be equal.

Here, AD = BC and AB = DC

Then ABCD is a parallelogram.

Theorem 4: In a parallelogram, opposite angles are equal.

In \mathrm{ABCD,\angle A=\angle C} and \angle B=\angle D

Theorem 5: In a quadrilateral, if each pair of opposite angles is equal, then it is said to be a parallelogram. This is the reverse of Theorem 4.

Theorem 6: The diagonals of a parallelogram bisect each other.

Here, AC and BD are the diagonals of the parallelogram ABCD.

So the bisect each other at the centre.

DE = EB and AE = EC

Theorem 7: When the diagonals of the given quadrilateral bisect each other, then it is a parallelogram.

This is the reverse of the theorem 6.

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