Parallelogram – Definition, Sorts, and Examples

A parallelogram is a particular quadrilateral with each pairs of reverse sides parallel as proven within the determine under.

Forms of parallelogram

Squares, rectangles, and rhombuses are additionally parallelograms, extra particularly particular parallelograms, since their reverse sides are parallel in response to 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. Due to this fact, a sq. is a rhombus and a rectangle on the identical time.  

Diagonal, base, altitude, and top of a parallelogram

The diagonal of a parallelogram is a line phase 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 under.

A base of a parallelogram is any of its sides. 

The altitude of a parallelogram is a line phase 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. Nevertheless, within the determine under, 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 test the lesson about properties of a parallelogram to study extra about these 5 properties of parallelograms.

Tips on how to assemble a parallelogram utilizing a straightedge and compass

You possibly can simply assemble a parallelogram by following rigorously 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 alter the opening of the compass to measure the size of phase BA. Then, conserving 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 alter the opening of the compass to measure the size of phase BC. Then, conserving 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 will have a parallelogram ABCD. The perimeter is the same as the sum of the lengths of its sides.

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

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

Perimeter = size of phase AB + size of phase AB + size of phase BC + size of phase BC

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

Space of a parallelogram

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

Let h be the size of the altitude.

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

Parallelogram FAQs

Are parallelograms trapezoids?

It is determined by which definition is used for a trapezoid! Parallelograms will need to have two pairs of reverse sides which might be parallel. Some textbooks say that trapezoids will need to have precisely one pair of parallel sides. If there’s precisely one pair of parallel sides, then the reply is not any. Different textbooks say that trapezoids will need to have at the very least one pair of parallel sides. On this case, all parallelograms are trapezoids since they match contained in the definition of trapezoids.

Are trapezoids parallelograms?

It is determined by which definition is used for a trapezoid! Parallelograms will need to have two pairs of reverse sides which might be parallel. Some textbooks say that trapezoids will need to have precisely one pair of parallel sides. If there’s precisely one pair of parallel sides, then the reply is not any. Different textbooks say that trapezoids will need to have at the very least one pair of parallel sides. On this case, some trapezoids might turn into parallelograms if these trapezoids have two pairs of reverse sides which might be parallel.

Do all of the angles in a parallelogram add as much as 360?

Sure! For those who add up the 4 angles in any parallelogram, it is going to equal to 360 levels.

Do all parallelograms have 4 proper angles?

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 referred to as a rectangle.

is each parallelogram a quadrilateral?

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