Quick and Easy RS Aggarwal Class 8 Mathematics Solutions for Chapter-16 Parallelograms

Q: 1. The ratio between two adjacent angles of a ||gm ABCD are in the ratio 1 : 4. Find the angles.

Let ∠ A = x and ∠ B = 4xBut ∠A + ∠B = 180°=> x + 4x = 180°=> 5x = 180°∴ x = 180/5= 36°∴ ∠A = Ax = 36°∠B = 4x = 4 x 36 = 144° Ans.

Q: 2. The sum of opposite angles of the parallelograms is 140°. Find the measure of all the angles.

In ||gm ABCD, ∠A and ∠C are opposite angles.∴ ∠A = ∠C= 140°But ∠A = ∠C (opposite angles)∴ ∠A = ∠C= 140°/2= 70°But ∠A + ∠B = 180°(sum of adjacent angles)=> 70° + ∠B = 180°=> ∠B = 180° – 70° = 110°But ∠ D = ∠ B (opposite angles)∴ ∠D = 110°Hence ∠A = 70°, ∠B = 110°, ∠C = 70° and ∠ D = 110° Ans.

Q: 3. ABCD is a parallelogram.AE and CF are the bisectors of ∠A and ∠C respectively. Prove that AE || CF.

In ∆ADE and ∆CBF,AD = BC(Opposite sides of the parallelogram)∠D = ∠B(Opposite angles of the parallelogram)∠DAE = ∠FCB (1/2 of equal angles)∴ ∆ADE ≅ ∆CBF(S.A.A. congruence)∴ DE = BF (c.p.c.t.)But CD = AB(Opposite sides of the parallelogram)∴ CD – DE = AB – BF=> EC = AFand AB || CD∴ AFCE is a parallelogram∴ AE || CF.

Q: 4. List some properties of a parallelogram and name one of its special types.

The properties of a parallelogram are-A parallelogram is a special type of quadrilateral, in which its opposite sides are parallel and equalThe opposite angles of the parallelogram are also equal.Adjacent angles in it are supplementary in nature, which means that the sum of two adjacent angles is equal to 180 degrees.The two Diagonals of a parallelogram bisects each other at their mid-pointsIf any of the interior angles is 90 degrees, then all of them will be right angles.Parallelograms are of various types, one such special type of it is Rhombus.

RS Aggarwal Solutions

Quick and Easy RS Aggarwal Class 8 Mathematics Solutions for Chapter-16 Parallelograms

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Class 8 RS Aggarwal Maths Parallelograms Solutions - Free PDF Download

The smartest thing to do to score well in your 10th board exams is to understand and make a strong foundation in class 9. For this, you can go through the RS Aggarwal Class 8 Maths Chapter 16 solutions specially made by the experts of mathematics from Vedantu which will be just the right resource for you. The RS Aggarwal Solutions Class 8 Chapter 16 will explain each problem most easily and understandably. It explains each of the sections in a detailed manner.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Download Class 8 Maths and Class 8 Science NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Download RS Aggarwal Solutions Class 8 Solutions Chapter 16 in PDF

The RS Aggarwal Class 8 Solutions Chapter 16 can be easily accessed from the official website of Vedantu. The most convenient way to do a quick revision is by using the RS Aggarwal Class 8 ch 16 Solution in a PDF. It is very convenient for students to do a quick revision anytime. They are very handy as they can be downloaded on your devices or printed out. This offline mode of parallelogram class 8 RS Aggarwal solutions is easily available and can be accessed even without an internet connection.

Parallelogram Class 8 RS Aggarwal Solutions

RS Aggarwal Solutions Class 8 Ch 16 is based on the concepts of Parallelogram. Some of the key topics discussed in this chapter are:

All angles of the parallelogram This theory suggests that all the angles of the parallelogram sums up to 360 degree.

The point A,B,C and D represent a parallelogram

∠A+∠B+ ∠C+∠D= 360

i. Theories of parallelogram

ii. The opposite sides of a parallelogram are equal.

iii. The opposite angles of a parallelogram are equal.

iv. Diagonals bisect each other.

Congruence of Triangles - The triangles are said to be congruent if the sides of the respective triangles superimpose the sides of the other sides.
The side of one of the triangles is equal to the corresponding side of the other triangle.

There are theories that prove that one triangle is congruent to another.

SSS - In this, the side of one triangle is equal to the other triangle's side. In triangle ABC and PQR,

AB= PQ

BC= QR

AC= PR

SAS - In this, one side is equal to the corresponding side, the angle is equal to the corresponding angle, and the side to the other triangle's side. In triangle ABC and PQR, AB= PQ

∠B= ∠Q

BC= QR

ASA - In this, an angle is equal to the corresponding angle of the triangle, and a side is equal to the corresponding side of the other triangle.

For example, In triangle ABC and PQR,

∠B= ∠Q

BC= QR

∠C= ∠R

AAS - In this, two angles are equal to the corresponding angles and the side is equal to the side.

For example, In triangle ABC and PQR,

∠A= ∠P

∠B= ∠Q

AB= PQ

HL - This applies to the right angle, In this, the hypotenuse of one right-angled triangle is equal to the other, and any of the other sides is equal to the side of the other right-angled triangle. For example, In right-angled triangles ABC and PQR,

AC= PR

BC= QR

The topics of class 8 maths parallelogram were discussed in the above pointers and have briefly described the theories and topics related to the parallelogram.

All the Exercise questions with solutions in Chapter-16 Parallelograms are given below:

Exercise (Ex 16A) 16.1

Exercise (Ex 16B )16.2

Preparation Tips for RS Aggarwal Class 8 Maths Chapter 16

Understand the figure very well and apply the theories to reach the solution.
Note down the different shapes involved in the figure as they are crucial for solving RS Aggarwal Solutions Class 8 Chapter 16.
If you solve all the sums of Class 8 Maths Parallelogram, it will give you enough practice on this topic to understand all the theories related to parallelogram.

Get the easiest solutions from Vedantu to prepare this chapter in the best way possible.

Download and refer to this file whenever you have a doubt in your mind. Keep yourself ahead of the class by utilizing the concepts used by the experts to solve the problems. Use the easy language of this solution file to learn how to answer questions quickly in the exams.

FAQs on Quick and Easy RS Aggarwal Class 8 Mathematics Solutions for Chapter-16 Parallelograms

1. The ratio between two adjacent angles of a ||gm ABCD are in the ratio 1 : 4. Find the angles.

Let ∠ A = x and ∠ B = 4x

But ∠A + ∠B = 180°

=> x + 4x = 180°

=> 5x = 180°

∴ x = 180/5= 36°

∴ ∠A = Ax = 36°

∠B = 4x = 4 x 36 = 144° Ans.

2. The sum of opposite angles of the parallelograms is 140°. Find the measure of all the angles.

In ||gm ABCD, ∠A and ∠C are opposite angles.

∴ ∠A = ∠C= 140°

But ∠A = ∠C (opposite angles)

∴ ∠A = ∠C= 140°/2= 70°

But ∠A + ∠B = 180°

(sum of adjacent angles)

=> 70° + ∠B = 180°

=> ∠B = 180° – 70° = 110°

But ∠ D = ∠ B (opposite angles)

∴ ∠D = 110°

Hence ∠A = 70°, ∠B = 110°, ∠C = 70° and ∠ D = 110° Ans.

3. ABCD is a parallelogram.AE and CF are the bisectors of ∠A and ∠C respectively. Prove that AE || CF.

In ∆ADE and ∆CBF,

AD = BC

(Opposite sides of the parallelogram)

∠D = ∠B

(Opposite angles of the parallelogram)

∠DAE = ∠FCB (1/2 of equal angles)

∴ ∆ADE ≅ ∆CBF

(S.A.A. congruence)

∴ DE = BF (c.p.c.t.)

But CD = AB

(Opposite sides of the parallelogram)

∴ CD – DE = AB – BF

=> EC = AF

and AB || CD

∴ AFCE is a parallelogram

∴ AE || CF.

4. List some properties of a parallelogram and name one of its special types.

The properties of a parallelogram are-

A parallelogram is a special type of quadrilateral, in which its opposite sides are parallel and equal
The opposite angles of the parallelogram are also equal.
Adjacent angles in it are supplementary in nature, which means that the sum of two adjacent angles is equal to 180 degrees.
The two Diagonals of a parallelogram bisects each other at their mid-points
If any of the interior angles is 90 degrees, then all of them will be right angles.

Parallelograms are of various types, one such special type of it is Rhombus.

5. How many exercises are there in the Chapter 16 parallelogram of class 8?

If you follow Vedantu’s solution for Chapter 16 Parallelogram of class 8 has only two exercises 16 A and 16 B. Exercise 16 A contains 14 and 16 B contains 10 questions. Solutions to all of which are available in the RS Aggarwal class 8 maths solutions for chapter 16 provided by the Vedantu. In 16 A, students will encounter questions regarding the properties of parallelograms. And in exercise 16 b, questions will be based on the properties of diagonals of square, rhombus, and parallelograms.