Parallelograms. Properties, Shapes, Sides, Diagonals and Angles-with examples and pictures


Properties, Shapes, Diagonals and Area

A parallelogram is quadrilateral comprised of two pairs of parallel lines. There are several rules involving

Interactive Parallelogram

The full size interactive parallelogram has additional features such as the lengths of the diagonals.

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Two Pairs of Parallel Lines

Parallelograms Shape and Properties

To create a parallelogram just think of 2 different pairs of parallel lines intersecting. ABCD is a parallelogram.

Click on the button below to turn the pure parallel lines into a parallelogram.

Parallelograms Shape and Properties

Angles of A Parallelogram

Opposite Angles are Congruent

Parallelogram Angles Picture

$$ \angle D \cong \angle B \\ \angle A \cong \angle C $$

Triangles can be used to prove this rule about the opposite angle.

Consecutive angles are supplementary

consecutive angles of a parallelogram

The following pairs of angles are supplementary

$$ \angle C $$ and $$ \angle D $$
$$ \angle C $$ and $$ \angle B $$
$$ \angle A $$ and $$ \angle B $$
$$ \angle A $$ and $$ \angle D $$

To explore these rules governing the angles of a parallelogram use Math Warehouse's interactive parallelogram.

Problem 1

What is the measure of angles A, B and C in parallelogram ABCD?

Picture Angles of Parallelogram

$$ \angle A = 80° $$ since opposite angles are congruent.

Since consecutive angles are supplementary

You can then find $$ \angle C $$ easily since it is opposite of $$ \angle B $$

$$ \angle C= 80° $$
Problem 2

What is the measure of x, y, z in parallelogram below?

Paralelogram Angles Diagram
Problem 3

In a parallelogram one of the angles measures 25°, what are the measures of the other angles?

Paralelogram Angles Diagram

Sides of a Parallelogram

Sides of Parallelogram The opposite sides of a parallelogram are congruent

Triangles can be used to prove this rule about the opposite sides.

To explore these rules governing the sides of a parallelogram use Math Warehouse's interactive parallelogram

Problem 4

What is the length of side BD and side CD in parallelogram ABCD?

Sides of Parallelogram Diagram
Problem 5

What is x in the parallelogram on the left?

Parallelogram Sides Picture
Sides Practice Problem
Problem 6

What is the value of x and y in the parallelogram below?

Sides Practice Problem

Since opposite sides are congruent you can set up the following equations:
2x − 10 = x + 80 and solve for x

x =90
3y − 4 = y + 20 and solve for y
y = 12

Diagonals of a Parallelogram

Parallelogram Diagonals Bisect Each Other

The diagonals of a parallelogram bisect each other


To explore these rules governing the diagonals of a parallelogram use Math Warehouse's interactive parallelogram

Problem 7

What is x and Y?

Parallelogram Diagonals

Since the diagonals bisect each other, y = 16 and x = 22

Problem 8

What is x?

Diagonals of Parallelogram DIagram

x + 40 = 2x + 18
40 = x +18
40 = x + 18
22 = x

Classify Quadrilateral as parallelogram (a classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral. Then ask the students to measure the angles, sides etc.. of inscribed shape and use the measurements to classify the shape(parallelogram).

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