RD Sharma Solutions for Class 8 Chapter 18 Practical Geometry (Constructions) Exercise 18.5

Exercise 18.5 Chapter 18, of RD Sharma, the concept of construction of a quadrilateral when its three angles and their two included sides are given are explained by our tutors with examples. The procedures to construct a quadrilateral are provided here with steps, which is very helpful for students to prepare for their exams. For further assistance, students can refer to RD Sharma Class 8 Solutions formulated by experts at BYJU’S which has all the shortcut methods to solve any question. For better understanding, students can download the pdf from the links provided below.

Download the Pdf of RD Sharma for Class 8 Maths Exercise 18.5 Chapter 18 Practical Geometry (Constructions)

 

rd sharma class 8 maths chapter 18 ex 5
rd sharma class 8 maths chapter 18 ex 5
rd sharma class 8 maths chapter 18 ex 5
rd sharma class 8 maths chapter 18 ex 5
rd sharma class 8 maths chapter 18 ex 5

 

Access answers to RD Sharma Maths Solutions For Class 8 Exercise 18.5 Chapter 18 Practical Geometry (Constructions)

1. Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.

Solution:

The given details are AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 4cm

Step 2- Construct and angle of 75o at A.

Step 3- Construct and angle of 80o at B.

Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C.

Step 5- Construct and angle of 120o at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 27

2. Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.

Solution:

The given details are AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.

We know that ∠A + ∠B + ∠C + ∠D = 360o

∴ ∠C = 105o

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 5.5cm

Step 2- Construct and angle of 60o at A.

Step 3- Construct and angle of 105o at B.

Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C.

Step 5- Construct and angle of 105o at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 28

3. Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

Solution:

The given details are PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

We know that ∠P + ∠Q + ∠R + ∠S = 360o

∴ ∠Q = 75o

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 3.5cm

Step 2- Construct and angle of 105o at P.

Step 3- Construct and angle of 75o at Q.

Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R.

Step 5- Construct and angle of 105o at R such that it meets the line segment PX, mark that point as S.

Step 6- Now join QR, RS and PS

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 29

4. Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

Solution:

The given details are BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

We know that ∠A + ∠B + ∠C + ∠D = 360o

∴ ∠C = 95o

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.5cm

Step 2- Construct and angle of 110o at B.

Step 3- Construct and angle of 95o at C.

Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D.

Step 5- Construct and angle of 85o at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 30

5. Construct a quadrilateral ABCD ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.

Solution:

The given details are ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.

We know that ∠A + ∠B + ∠C + ∠D = 360o

∴ ∠D = 115o

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.7cm

Step 2- Construct and angle of 105o at B.

Step 3- Construct and angle of 105o at C.

Step 4- Cut an arc of radius 6.8cm with C as the center to mark that point as D.

Step 5- Construct and angle of 115o at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 31

6. Construct a quadrilateral PQRS in which PQ = 4 cm, QR = 5 cm ∠P = 50°, ∠Q = 110° and ∠R = 70°.

Solution:

The given details are PQ = 4 cm, QR = 5 cm ∠P = 50°, ∠Q = 110° and ∠R = 70°.

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 4cm

Step 2- Construct and angle of 50o at P.

Step 3- Construct and angle of 110o at Q.

Step 4- Cut an arc of radius 5cm with Q as the center to mark that point as R.

Step 5- Construct and angle of 70o at R such that it meets the line segment PX, mark that point as S.


Step 6- Now join QR, RS and PS

RD Sharma Solutions for Class 8 Maths Chapter 18 – Practical Geometry (Constructions) image - 32


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