Question

How to prove quadrilaterals are parallelograms?

Answer 1

AB: 24

BC: 15

CD: 24

AD: 15

Explanation:

A quadrilateral is any shape with four sides. A parallelogram has four sides, therefore it is classified as a quadrilateral.

The opposite sides of a parallelogram are equal to each other, so make the opposite sides of this parallelogram equal to each other in an equation.

AB = DC

• 2y + 2 = 3y - 9

AD = BC

• 3x + 6 = y + 4

Now you have a system of equations that you can solve by substitution.

Solve for y in the first equation by subtracting 2 from both sides.

• 2y = 3y - 11

Subtract 3y from both sides of the equation.

• -y = -11

Divide both sides of the equation by negative 1 to make y a positive number.

• y = 11

Substitute this value of y into the second equation we made.

3x + 6 = (11) + 4

Combine like terms on the right side of the equation then subtract 6 from what you get.

• 3x = 9

Divide both sides of the equation by 3.

• x = 3

To find the length of each side of the parallelogram, substitute x into AD and y into AB.

• AD: 3(3) + 6 = 15
• AB: 2(11) + 2 = 24

Since AD = BC and AB = DC, you know the lengths for these sides as well.