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Parallelograms

Properties, Shapes, Diagonals and Area

A parallelogram is quadrilateral comprised of two pairs of parallel lines. There are several rules involving
This Page: Angles | Sides | Diagonals |Interactive Parallelogram
Interactive Parallelogram
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The full size interactive parallelogram has additional features such as the lengths of the diagonals.

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Parallelograms Shape and Properties

Two Pairs of Parallel Lines

To create a paralleogram, just think of 2 different pairs of parallel lines intersecting.
ABCD is a parallelogram.
Parallelograms Shape and Properties Click on the button below to turn the pure parallel lines into a parallelogram.
Make Parallelogram

Angles of A Parallelogram

Opposite Angles are Congruent

Parallelogram Angles Picture
pair1
pair1
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
h C and g C
f C and e B
d A and c B
b A and a D
To explore these rules governing the angles of a parallelogram use Math Warehouse's interactive parallelogram.


What is the measure of angles A, B and C in parallelogram ABCD?
Answer
b A= 80° since opposite angles are congruent

Since consecutive angles are supplementary.
f

You can then find aC easily since it is opposite of a B
b C= 80°
Picture Angles of Parallelogram  

What is the measure of x, y, z in parallelogram below?
Answer
Paralelogram Angles Diagram
In a parallelogram one of the angles measures 25°, what are the measures of the other angles?
Answer

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
Sides of Parallelogram Diagram What is the length of side BD and side CD in parallelogram ABCD?
Answer
Parallelogram Sides Picture What is x in the parallelogram on the left?
Answer
What is the value of x and y in the parallelogram below?
Answer
Sides of Parallelogram Illlustration

Diagonals of a Parallelogram

Parallelogram Diagonals Bisect Each Other The diagonals of a parallelogram bisect each other
AO = OD
CO = OB
To explore these rules governing the diagonals of a parallelogram use Math Warehouse's interactive parallelogram
What is x and Y?
Answer

Parallelogram Diagonals
What is x?
Answer
Diagonals of Parallelogram DIagram
Properties of parallelograms: Angles | Sides | Diagonals |Interactive Parallelogram | top
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).

Types of Parallelograms: rectangle | rhombus | square | rectangle vs. square | comparison of properties of each type of parallogram | Criteria prove quadrilateral is a parallelogram