# Properties of a parallelogram

The properties of a parallelogram are listed below. We will use a parallelogram ABCD to show these properties. 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 and bisects diagonal BD ( red line ) at E. 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

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.

## Using the properties of a parallelogram to solve math problems

Example  #1: Use the parallelogram below to find the length of segment BC and segment AD. Since the opposite sides of a parallelogram are congruent, the length of segment BC is equal to the length of segment AD.

4x - 10 = 3x + 5.

Subtract 3x from each side

4x - 3x - 10 = 3x - 3x + 5

Simplify each side

x - 10 = 5

Add 10 to both sides of the equation.

x - 10 + 10 = 5 + 10

Simplify

x = 15

BC = AD = 4x - 10 = 4 times 15 - 10 = 60 - 10 = 50

Example  #2: Use the parallelogram below to find the length of segment AC and segment BD. Since the diagonals of a parallelogram bisect each other, we get the following results:

• The length of segment AI is equal to the length of segment CI
• The length of segment BI is equal to the length of segment DI

This leads to a system of linear equations to solve

2y - 4 = 4x

y = x + 4

Substitute x + 4 for y in 2y - 4 = 4x

2(x + 4) - 4 = 4x

Distribute

2x + 8 - 4 = 4x

Simplify

2x + 4 = 4x

Subtract 2x from each side

2x - 2x + 4 = 4x - 2x

Simplify

4 = 2x

x = 4/2 = 2

y = x + 4 = 2 + 4 = 6

AC = AI + CI = 2y - 4 + 4x = 2×6 - 4 + 4×2 = 12 - 4 + 8 = 16

BD = BI + DI = x + 4 + y = 2 + 4 + 6 = 12

## Recent Articles 1. ### Hourly to Salary Calculator - Convert Hourly Wage to a Salary

Jan 20, 20 05:26 PM

Hourly to salary calculator- Convert your income to a yearly salary or a monthly salary

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.