Properties of a Parallelogram

Parallelograms are two-dimensional geometrical shapes where both pairs of opposite sides are parallel and equal. It is a type of quadrilateral. Parallelograms have various real-life applications like engineering design for structures as well as in physics for visually adding or subtracting vectors due to their parallel sides and diagonal bisection. In this detailed guide, we will look at the properties of parallelogram class 9 as well as compare and contrast the properties of a parallelogram and rectangle with figures for better understanding. 

1.0What is a Parallelogram?

In simple words, a parallelogram is a flat shape where both opposite sides are parallel and equal to the length. Squares, rectangles, and rhombuses are special types of parallelograms. It exhibits several important properties related to its angles, sides, and diagonals, which we will discuss in detail. 

2.0Properties of a Parallelogram

The six properties of a parallelogram are related to its angles, sides, and diagonals. Keep reading to thoroughly understand the key 6 properties of a parallelogram. 

1. Opposite Sides are Equal

One defining characteristic of a parallelogram is that the opposite sides of a parallelogram are always equal and parallel to each other. 

Mathematically:

If ABCD is a parallelogram, then: $AB=CDandAD=BC$

2. Opposite Sides are Parallel

The opposite sides of a parallelogram are parallel to each other.

Mathematically: $ABIIDCandADIIBC.$

3. Opposite Angles are Equal

The angle properties of parallelograms state that the opposite angles of a parallelogram are equal in measure. 

Mathematically: $\angle A=\angle C\text{and}\angle B=\angle D$

4. Adjacent Angles are Supplementary

Each pair of adjacent angles in a parallelogram is supplementary, which means it adds up to 180°. 

Mathematically: $\angle A+\angle B=180^{\circ }\text{and}\angle C+\angle D=180^{\circ }$

5. Diagonals Bisect Each Other

According to parallelogram properties diagonal, each diagonal of a parallelogram intersects at a midpoint and divides each diagonal into two congruent segments. 

If E is the midpoint of the diagonal intersection, then AE = EC and BE = ED.

6. Each Diagonal Bisects the Parallelogram

Each diagonal of any given parallelogram divides it into two congruent triangles.

Mathematically, $△CDA\cong △ABC\text{and}△BAD\cong △DCB$

What are the Four Properties of a Parallelogram?

To answer the question, what are the four properties of parallelogram? We have made note of the most essential properties of a parallelogram. These four properties are the most crucial points, and all the information learnt previously boils down to this:

• The opposite sides of any given parallelogram are equal & parallel to each other.
• The opposite angles of every parallelogram are equal.
• The diagonals of a parallelogram bisect each other.
• The consecutive angles of a parallelogram are supplementary. 

These four properties are the foundation of a parallelogram.

3.0Properties of a Parallelogram with Figure

To better visualise the concepts, let’s look at the properties of a parallelogram with figure. It will help us realise how the theoretical concept applies to geometrical problems. Let’s consider the parallelogram ABCD from the figure below and understand the properties.

• AB = CD & AD = BC (Opposite sides are equal)
• ∠A = ∠C & ∠B = ∠D (Opposite angles are equal)
• ∠A + ∠B = 180° (Consecutive angles are supplementary)
• Diagonals AC and BD bisect each other at the midpoint E.

4.0Properties of a Parallelogram and Rectangle

A rectangle is a special kind of parallelogram with additional properties. Let’s compare and contrast the properties of a parallelogram and rectangle in the below table:

Property	Parallelogram	Rectangle
Opposite sides equal	Yes	Yes
Opposite angles equal	Yes	Yes
Consecutive angles	Supplementary (180°)	90° angles
Diagonals bisect each other	Yes	Yes
Diagonals are equal	Not necessarily	Always
All angles 90°	No	Yes
Diagram

Rectangles are parallelograms with all 90° angles and equal diagonals. Hence, it can be said that every rectangle is a parallelogram, but not every parallelogram is a rectangle. 

5.0Conclusion

Understanding the properties of parallelogram class 9 is crucial to building the basework for the advanced geometry of the boards. Understand the basics thoroughly and apply these properties to solving real-life problems to ace the topic.