Home Math Parallelogram – Definition, Varieties, and Examples

### Parallelogram – Definition, Varieties, and Examples

A parallelogram is a particular quadrilateral with each pairs of reverse sides parallel as proven within the determine beneath. Discover that the other sides which are parallel traces are proven utilizing the identical quantity of arrow heads.

## Varieties of parallelogram

Squares, rectangles, and rhombuses are additionally parallelograms, extra particularly particular parallelograms, since their reverse sides are parallel in accordance with the definition.

A rhombus is a parallelogram with 4 equal sides.

A rectangle is a parallelogram with 4 proper angles

A sq. is a parallelogram with 4 equal sides and 4 proper angles. Subsequently, a sq. is a rhombus and a rectangle on the similar time.

## Diagonal, base, altitude, and top of a parallelogram

The diagonal of a parallelogram is a line section that joins two vertices that aren’t subsequent to one another. A parallelogram has two diagonals. The diagonals are proven in black within the determine beneath.

A base of a parallelogram is any of its sides.

The altitude of a parallelogram is a line section that begins from a vertex and is both perpendicular to the bottom or to the road containing the bottom.

Within the determine above, the altitude is perpendicular to the bottom. Nonetheless, within the determine beneath, the altitude is perpendicular to the road containing the bottom.

The peak of a parallelogram is the size of an altitude.

## Properties of parallelogram

• Reverse sides of a parallelogram are congruent.
• Reverse angles of a parallelogram are congruent.
• The diagonals of a parallelogram bisect one another.
• Consecutive angles are supplementary or add as much as 180 levels.
• Every diagonal of a parallelogram turns the parallelogram into 2 congruent triangles.

Please examine the lesson about properties of a parallelogram to study extra about these 5 properties of parallelograms.

## How you can assemble a parallelogram utilizing a straightedge and compass

You possibly can simply assemble a parallelogram by following fastidiously the next 4 easy steps.

Step 1

Draw an angle ABC of any measure

Step 2

Put the needle of a compass at level B and modify the opening of the compass to measure the size of section BA. Then, preserving the opening of the compass the identical, put the needle of the compass at level C and draw an arc.

Step 3

Put the needle of a compass at level B and modify the opening of the compass to measure the size of section BC. Then, preserving the opening of the compass the identical, put the needle of the compass at level A and draw an arc.

Step 4

Label the purpose of intersection of the 2 arcs D. Then, draw line segments AD and CD.

## Perimeter of a parallelogram

Suppose you’ve a parallelogram ABCD. The perimeter is the same as the sum of the lengths of its sides.

The size of section AB is the same as the size of section CD.

The size of section BC is the same as the size of section AD.

Perimeter = size of section AB + size of section AB + size of section BC + size of section BC

Perimeter = 2(size of section AB) + 2(size of section BC)

## Space of a parallelogram

The world of a parallelogram is the product of the bottom and the size of the altitude.

Let h be the size of the altitude or the peak of the parallelogram.

Then, the system to make use of to search out the world of a parallelogram is space = b × h

Discover that the time period base refers each to the size of the bottom and the section.

### Parallelogram FAQs

It will depend on which definition is used for a trapezoid! Parallelograms should have two pairs of reverse sides which are parallel. Some textbooks say that trapezoids should have precisely one pair of parallel sides. If there may be precisely one pair of parallel sides, then the reply is not any. Different textbooks say that trapezoids should have a minimum of one pair of parallel sides. On this case, all parallelograms are trapezoids since they match contained in the definition of trapezoids.

It will depend on which definition is used for a trapezoid! Parallelograms should have two pairs of reverse sides which are parallel. Some textbooks say that trapezoids should have precisely one pair of parallel sides. If there may be precisely one pair of parallel sides, then the reply is not any. Different textbooks say that trapezoids should have a minimum of one pair of parallel sides. On this case, some trapezoids might develop into parallelograms if these trapezoids have two pairs of reverse sides which are parallel.

Sure! If you happen to add up the 4 angles in any parallelogram, it’ll equal to 360 levels.

No! A parallelogram will find yourself having 4 proper angles if simply one of many angles is a proper angle. On this case, it’s known as a rectangle.

A quadrilateral is a polygon with 4 sides. Since each parallelogram has 4 sides, each parallelogram can also be a quadrilateral.

Within the American time period, a trapezium is a quadrilateral that has no parallel sides. It’s form of the “reverse” of a parallelogram which has two pairs of parallel sides.