Properties of parallelograms

Three quick questions from earlier lessons.

A diagonal cuts a parallelogram into two triangles. Are they congruent?

Properties of parallelograms.

In a parallelogram: opposite sides are equal, opposite angles are equal, consecutive angles add to

180^\circ

, and the diagonals bisect each other.

Parallelogram with $\angle A = 72^\circ$ and diagonal $BD = 18$ .

\angle C = 72^\circ

Opposite angle.

\angle B = \angle D = 108^\circ

Consecutive.

BM = 9

Diagonals bisect each other.

Your turn: $\angle B = 125^\circ$ . Find $\angle C$ .

55^\circ

Consecutive: 180 − 125.

In parallelogram $ABCD$ , $\angle A = 42^\circ$ . Find $\angle B$ , in degrees.
In parallelogram $ABCD$ , $\angle A = 139^\circ$ . Find $\angle B$ , in degrees.

The diagonals of parallelogram $ABCD$ meet at $M$ , and $AC = 18$ . Find $AM$ .Not to scale

In parallelogram $ABCD$ , $AB = 2x + 3$ and $CD = x + 8$ . Find $x$ .Not to scale

Boss problem. In parallelogram $ABCD$ , $\angle A = (3x + 9)^\circ$ and $\angle C = (x + 45)^\circ$ .

Three questions to check you have got it.

In parallelogram $ABCD$ , $\angle A = 42^\circ$ . Find $\angle B$ , in degrees.
In parallelogram $ABCD$ , $\angle A = 139^\circ$ . Find $\angle B$ , in degrees.
In parallelogram $ABCD$ , $\angle A = 41^\circ$ . Find $\angle B$ , in degrees.

Parallelograms

Opposite sides and angles equal; consecutive angles 180°; diagonals bisect each other.

Watch out: opposite (equal) vs consecutive (supplementary).

End of the lesson