Exercise 18.2 deals with concepts related to constructing a quadrilateral when its three sides and two diagonals are given. Students can improve their conceptual understanding of the chapter by solving the solutions formulated by our subject experts. Students aspiring to score high marks are advised to download and practise the solutions on a daily basis. RD Sharma Class 8 Solutions PDF is available here, which students can download from the links provided below.
RD Sharma Solutions for Class 8 Maths Exercise 18.2 Chapter 18 Practical Geometry (Constructions)
Access answers to RD Sharma Maths Solutions for Class 8 Exercise 18.2 Chapter 18 Practical Geometry (Constructions)
1. Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm.
Solution:
The given details are AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line AC = 6cm.
Step 2- Cut an arc of radius 3.8cm with A as the centre to mark that point as B.
Step 3- Cut an arc of radius 3cm with C as the centre to intersect with point B.
Step 4- Cut an arc of radius 3.8cm with B as the centre to mark that point as D.
Step 5- Cut an arc of radius 2.3cm with A as the centre to intersect with point D.
Step 6- Now join AB, BD, AD and DC.
2. Construct a quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.
Solution:
The given details are BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line AC = 6cm.
Step 2- Cut an arc of radius 6cm with A as the centre to mark that point as D.
Step 3- Cut an arc of radius 5cm with C as the centre to intersect at point D.
Step 4- Cut an arc of radius 10cm with D as the centre to mark that point as B.
Step 5- Cut an arc of radius 7.5cm with C as the centre to intersect at point B.
Step 6- Now join AD, CD, DB and AB
3. Construct a quadrilateral ABCD when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.
Solution:
The given details are AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.
Consider a triangle ABD from the given data,
So, AB + BD = 3+4 = 7cm
We know that sum of lengths of two sides of a triangle is always greater than the third side.
∴ The construction is not possible.
4. Construct a quadrilateral ABCD given AD = 3.5 cm, BC = 2.5 cm, CD = 4.1 cm, AC = 7.3 cm and BD = 3.2 cm.
Solution:
The given details are AD = 3.5 cm, BC = 2.5 cm, CD = 4.1 cm, AC = 7.3 cm and BD = 3.2 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line CD = 4.1cm
Step 2- Cut an arc of radius 7.3cm with C as the centre to mark that point as A.
Step 3- Cut an arc of radius 3.5cm with D as the centre to intersect at point A.
Step 4- Cut an arc of radius 3.2cm with D as the centre to mark that point as B.
Step 5- Cut an arc of radius 2.5cm with C as the centre to intersect at point B.
Step 6- Now join CA, DA, DB, CB and AB.
5. Construct a quadrilateral ABCD given AD = 5 cm, AB = 5.5 cm, BC = 2.5 cm, AC = 7.1 cm and BD = 8 cm.
Solution:
The given details are AD = 5 cm, AB = 5.5 cm, BC = 2.5 cm, AC = 7.1 cm and BD = 8 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line AB = 5.5cm
Step 2- Cut an arc of radius 2.5cm with B as the centre to mark that point as C.
Step 3- Cut an arc of radius 7.1cm with A as the centre to intersect at point C.
Step 4- Cut an arc of radius 8cm with B as the centre to mark that point as D.
Step 5- Cut an arc of radius 5cm with A as the centre to intersect at point D.
Step 6- Now join BC, AC, BD, AD and CD.
6. Construct a quadrilateral ABCD in which BC = 4 cm, CA = 5.6 cm, AD = 4.5 cm, CD = 5 cm and BD = 6.5 cm.
Solution:
The given details are BC = 4 cm, CA = 5.6 cm, AD = 4.5 cm, CD = 5 cm and BD = 6.5 cm.
Steps to construct a quadrilateral:
Step 1- Draw a line BC = 4cm
Step 2- Cut an arc of radius 6.5cm with B as the centre to mark that point as D.
Step 3- Cut an arc of radius 5cm with C as the centre to intersect at point D.
Step 4- Cut an arc of radius 5.6cm with C as the centre to mark that point as A.
Step 5- Cut an arc of radius 4.5cm with D as the centre to intersect at point A.
Step 6- Now join BD, CD, CA, DA and AB.
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