NCERT Solutions for Exercise 9.1 Class 9 Maths Chapter 9 - Areas Of Parallelograms And Triangles

# NCERT Solutions for Exercise 9.1 Class 9 Maths Chapter 9 - Areas Of Parallelograms And Triangles

Edited By Safeer PP | Updated on Jul 18, 2022 03:13 PM IST

NCERT Solutions for Class 9 Maths exercise 9.1 - The properties of parallelograms on the same base and between the same parallels are identified in NCERT solutions for Class 9 Maths chapter 9 exercise 9.1. It includes questions about the diagonal of a parallelogram, its base, side lengths, area, and other unique properties of parallelograms. More such properties of this geometric shape are addressed in this NCERT exercise. Class 9 Maths chapter 9 exercise 9.1 two shapes are stated to be on the common base and between the same parallels if: A side is common between two shapes. The vertices opposite the same side and the sides parallel to the common base are both on the same straight line parallel to the base.

If two shapes are congruent then the amount of area occupied by them will also be equal but the vice-versa of this statement is not true i.e. two figures having the same area need not be congruent.

A parallelogram is a geometrical shape with sides that are parallel to each other in two dimensions. It's a four-sided polygon (also known as a quadrilateral) with two parallel sides that are the same length. A parallelogram's interior opposite angles are also equal. The sum of a parallelogram's adjacent angles is 180 degrees.

## Areas Of Parallelograms And Triangles Class 9 Chapter 9 Exercise: 9.1

In figure (i), (iii) and (v) we can see that. they lie on the same base and between the same parallel lines.
In figure (i) figure (iii) figure (v)
Common base DC QR AD
Two parallels DC and AB QR and PS AD and BQ

## More About NCERT Solutions for Class 9 Maths Exercise 9.1

Area of the parallelogram are equals if they have a common base and between the same parallel line. We can also prove this property mathematical because we know that formula of the area of a parallelogram is the product of base and height. Since we have a base in the same and the distance between two parallel lines remains the same so the height is also the same.

The same theorem also applies to the triangles. Triangles with an equal area are those that have the same or common base and are connected by the same parallels.

Benefits of NCERT Solutions for Class 9 Maths Exercise 9.1

• Exercise 9.1 Class 9 Maths, is based on the AREAS OF PARALLELOGRAMS AND TRIANGLES by providing a general approach to calculate the area.

• Class 9 Maths chapter 9 exercise 9.1 introduces us to a new concept of parallelograms on the same base and between the same parallels

• Understanding the concepts from Class 9 Maths chapter 9 exercise 9.1 will allow us to understand the concepts related to AREAS OF PARALLELOGRAMS AND TRIANGLEs which are yet to come in the further exercise.

Also, See

## Subject Wise NCERT Exemplar Solutions

### Frequently Asked Questions (FAQs)

1. What is the main concept of NCERT solutions for Class 9 Maths exercise 9.1?

In this exercise, we learn about dealings with areas related to triangles and parallelograms especially if they are on the common base and between the same parallels.

2. If two figures A and B are congruent then what is the relation between their areas?

If figure A and figure B are congruent to each other then:

Area of (A) = Area of (B)

3. What do you understand by area of a given surface?

The area of a given surface is defined as the space occupied by the surface.

4. What is the area of a square?

The area of a given surface is defined as the space occupied by the surface.

5. What do you mean by figures on the same base?

Two figures are said to be on the same base if they both have one common side as their base.

6. What do you understand by figures on the same base and between the same parallels?

Two figures are supposed to be on the same base and between the same parallels in the event that the two of them have one common side as their base and the vertices which are inverse(opposite) to the normal base lie on both lie in a parallel line.

7. Fund the area of a rectangle with sides 6cm and 5cm?

Two figures are supposed to be on the same base and between the same parallels in the event that the two of them have one common side as their base and the vertices which are inverse(opposite) to the normal base lie on both lie in a parallel line.

8. Can we consider rectangle as a parallelogram?

Yes, we can consider a rectangle as a parallelogram as both of its opposite sides are parallel to each other.

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