Properties of a parallelogram


The properties of a parallelogram are listed below. We will use a parallelogram ABCD.


Parallelogram ABCD



Property #1

Opposite sides of a parallelogram are congruent.

The length of AB is equal to the length of DC
The length of BC is equal to the length of AD


Property #2

Opposite angles of a parallelogram are congruent.

Angle A is equal to angle C
Angle B = angle D


Property #3

The diagonals of a parallelogram bisect each other.

Diagonal AC ( red line ) intersects diagonal BD ( red line ) at E

Diagonals of a parallelogram


Property #4

Consecutive angles are supplementary or add up to 180 degrees

Angle A + angle B = 180 degrees
Angle B + angle C = 180 degrees
Angle C + angle D = 180 degrees
Angle D + angle A = 180 degrees

Congruent triangles of a parallelogram



Property #5

Each diagonal of a parallelogram turns the parallelogram into 2 congruent triangles

Triangle ABC is congruent or identical to triangle ADC
Triangle BCD is congruent or identical to triangle BAD




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