{"id":546310,"date":"2021-10-06T09:15:02","date_gmt":"2021-10-06T09:15:02","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=546310"},"modified":"2021-10-07T06:06:58","modified_gmt":"2021-10-07T06:06:58","slug":"rd-sharma-solutions-for-class-8-maths-chapter-18-practical-geometry-constructions","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-8-maths-chapter-18-practical-geometry-constructions\/","title":{"rendered":"RD Sharma Solutions for Class 8 Maths Chapter 18\u2013Practical Geometry (Constructions)"},"content":{"rendered":"\n

Class 8: Maths Chapter 18 solutions. Complete Class 8 Maths Chapter 18 Notes.<\/p>\n\n\n\n

RD Sharma Solutions for Class 8 Maths Chapter 18\u2013Practical Geometry (Constructions)<\/h2>\n\n\n\n

RD Sharma 8th Maths Chapter 18, Class 8 Maths Chapter 18 solutions<\/p>\n\n\n\n

EXERCISE 18.1 PAGE NO: 18.4<\/p>\n\n\n\n

1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 cm.<\/p>\n\n\n\n

Divide the quadrilateral into two triangles i.e., \u0394ABD and \u0394BCD<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm.<\/p>\n\n\n\n

Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as centre and radius CD = 6.4 cm.<\/p>\n\n\n\n

Step 3- Now join the intersection point from B and D and label it as C.<\/p>\n\n\n\n

Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. Do the same by taking D as center and radius DA = 3.8cm.<\/p>\n\n\n\n

Step 5- Join the intersection point from B and D and label it as A.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm Measure BD.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm Measure BD.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line segment AB = 5.5cm<\/p>\n\n\n\n

Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C.<\/p>\n\n\n\n

Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C.<\/p>\n\n\n\n

Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D.<\/p>\n\n\n\n

Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D.<\/p>\n\n\n\n

Step 6- Now join BC, CD and AD<\/p>\n\n\n\n

Measure of BD is 5.1cm.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 cm, WX = 3 cm and XZ = 9 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are XY = 5cm, YZ = 6cm, ZW = 7cm, WX = 3cm and XZ = 9cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw line XZ of length 9cm.<\/p>\n\n\n\n

Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z as centre and radius ZY = 6cm.<\/p>\n\n\n\n

Step 3- Now join the intersection point from X and Z and label it as Y.<\/p>\n\n\n\n

Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. Similarly, taking Z as the center and radius ZW = 7cm.<\/p>\n\n\n\n

Step 5- Join the intersection point from X and Z and label it as W.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

4. Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm, and QS = 8.2 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are PQ = 5.2 cm, PR = 6.8 cm, and QS = 8.2 cm.<\/p>\n\n\n\n

Steps to construct a parallelogram:<\/p>\n\n\n\n

Step 1- Draw line QS of length 8.2 cm.<\/p>\n\n\n\n

Step 2- Divide the line segment QS into half i.e 4.1 cm and mark that point as O. Now by taking O as center cut an arc on both the sides of O with a radius of 3.4cm each. And mark that points as P and R.<\/p>\n\n\n\n

Step 3- cut an arc by taking Q as a center and radius QR = 5.2cm to intersect with point R.<\/p>\n\n\n\n

Step 4- cut an arc by taking Q as a center and radius QP = 5.2cm to intersect with point P.<\/p>\n\n\n\n

Step 5- Join sides PQ, PS, QR and RS.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

5. Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other diagonal.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are side 6 cm and one diagonal 8 cm.<\/p>\n\n\n\n

We know all the sides of a rhombus are equal and diagonals bisect each other.<\/p>\n\n\n\n

Steps to construct a rhombus:<\/p>\n\n\n\n

Step 1- Draw a line XZ of length 8 cm.<\/p>\n\n\n\n

Step 2- By taking a radius of 6 cm, cut an arc by taking X as the center. Do the same by taking Z as centre with radius of 6 cm.<\/p>\n\n\n\n

Step 3- Now join the intersection point from X and Z and label it as Y.<\/p>\n\n\n\n

Step 4- Now for vertex W, by taking radius of 6 cm and cut an arc by taking X as the center. Do the same by taking Z as center and radius of 6 cm.<\/p>\n\n\n\n

Step 5- Join the intersection point from X and Z and label it as W.<\/p>\n\n\n\n

Step 6- Now join XY, XW, XZ and ZY<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

6. Construct a kite ABCD in which AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm.<\/p>\n\n\n\n

Steps to construct a kite:<\/p>\n\n\n\n

Step 1- Draw line AC of length 7.2 cm.<\/p>\n\n\n\n

Step 2- By taking a radius of 4 cm and cut an arc by taking A as the center. Do the same by taking C as centre with radius of 4.9 cm.<\/p>\n\n\n\n

Step 3- Now join the intersection point from A and C and label it as B.<\/p>\n\n\n\n

Step 4- Now for vertex D, cut an arc by taking A as the center. Do the same by taking C as center with radius of 4.9 cm.<\/p>\n\n\n\n

Step 5- Join the intersection point from A and C and label it as D.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

7. Construct, if possible, a quadrilateral ABCD given AB = 6 cm, BC = 3.7 cm, CD = 5.7 cm, AD = 5.5 cm and BD = 6.1 cm. Give reasons for not being able to construct it, if you cannot.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 6 cm, BC = 3.7 cm, CD = 5.7 cm, AD = 5.5 cm and BD = 6.1 cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB of length 6cm.<\/p>\n\n\n\n

Step 2- With A as a center cut an arc of radius 5.5cm and mark that point as D.<\/p>\n\n\n\n

Step 3- With B as a center cut an arc of radius 6.1cm to intersect with point D.<\/p>\n\n\n\n

Step 4- With B as a center cut an arc of radius 3.7cm and mark that point as C.<\/p>\n\n\n\n

Step 5- With D as a center cut an arc of radius 5.7cm to intersect with point C.<\/p>\n\n\n\n

Step 6- Now join AD, BD, BC and DC<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

8. Construct, if possible, a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm, CD = 3 cm, AD = 5.5 cm and AC = 11 cm. Give reasons for not being able to construct, if you cannot. (Not possible, because in triangle ACD, AD + CD<AC).<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 6 cm, BC = 7 cm, CD = 3 cm, AD = 5.5 cm and AC = 11 cm.<\/p>\n\n\n\n

Such a Quadrilateral cannot be constructed because, in a triangle, the sum of the length of its two sides must be greater than that of the third side.<\/p>\n\n\n\n

In triangle ACD,<\/p>\n\n\n\n

AD + CD = 5.5 + 3 = 8.5 cm<\/p>\n\n\n\n

Given, AC = 11 cm<\/p>\n\n\n\n

So, AD + CD < AC which is not possible.<\/p>\n\n\n\n

\u2234 The construction is not possible<\/p>\n\n\n\n

\n\n\n\n

EXERCISE 18.2 PAGE NO: 18.6<\/p>\n\n\n\n

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.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AC = 6cm.<\/p>\n\n\n\n

Step 2- Cut an arc of radius 3.8cm with A as the center to mark that point as B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3cm with C as the center to intersect with point B.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 3.8cm with B as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 2.3cm with A as the center to intersect with point D.<\/p>\n\n\n\n

Step 6- Now join AB, BD, AD and DC<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2. Construct a quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AC = 6cm.<\/p>\n\n\n\n

Step 2- Cut an arc of radius 6cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 5cm with C as the center to intersect at point D.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 10cm with D as the center to mark that point as B.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 7.5cm with C as the center to intersect at point B.<\/p>\n\n\n\n

Step 6- Now join AD, CD, DB and AB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. Construct a quadrilateral ABCD when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.<\/p>\n\n\n\n

Consider a triangle ABD from the given data,<\/p>\n\n\n\n

So, AB + BD = 3+4 = 7cm<\/p>\n\n\n\n

We know that sum of lengths of two sides of a triangle is always greater than the third side.<\/p>\n\n\n\n

\u2234 The construction is not possible.<\/p>\n\n\n\n

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.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line CD = 4.1cm<\/p>\n\n\n\n

Step 2- Cut an arc of radius 7.3cm with C as the center to mark that point as A.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3.5cm with D as the center to intersect at point A.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 3.2cm with D as the center to mark that point as B.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 2.5cm with C as the center to intersect at point B.<\/p>\n\n\n\n

Step 6- Now join CA, DA, DB, CB and AB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AD = 5 cm, AB = 5.5 cm, BC = 2.5 cm, AC = 7.1 cm and BD = 8 cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 5.5cm<\/p>\n\n\n\n

Step 2- Cut an arc of radius 2.5cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 7.1cm with A as the center to intersect at point C.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 8cm with B as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 5cm with A as the center to intersect at point D.<\/p>\n\n\n\n

Step 6- Now join BC, AC, BD, AD and CD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are BC = 4 cm, CA = 5.6 cm, AD = 4.5 cm, CD = 5 cm and BD = 6.5 cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line BC = 4cm<\/p>\n\n\n\n

Step 2- Cut an arc of radius 6.5cm with B as the center to mark that point as D.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 5cm with C as the center to intersect at point D.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 5.6cm with C as the center to mark that point as A.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4.5cm with D as the center to intersect at point A.<\/p>\n\n\n\n

Step 6- Now join BD, CD, CA, DA and AB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\n\n\n\n

EXERCISE 18.3 PAGE NO: 18.8<\/p>\n\n\n\n

1. Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, AD = 5 cm and \u2220B = 80\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, AD = 5 cm and \u2220B = 80\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 3.8cm<\/p>\n\n\n\n

Step 2- Construct and angle of 80o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3.4cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 5cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4.5cm with C as the center to intersect at point D.<\/p>\n\n\n\n

Step 6- Now join BC, AD and CD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2. Construct a quadrilateral ABCD given that AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and \u2220A = 45\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and \u2220A = 45\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 8cm<\/p>\n\n\n\n

Step 2- Construct and angle of 45o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 10cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 10cm with D as the center to mark that point as C.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 8cm with B as the center to intersect at point C.<\/p>\n\n\n\n

Step 6- Now join AD, DC and BC<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. Construct a quadrilateral ABCD in which AB = 7.7 cm, BC = 6.8 cm, CD = 5.1 cm, AS = 3.6 cm and \u2220C = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 7.7 cm, BC = 6.8 cm, CD = 5.1 cm, AS = 3.6 cm and \u2220C = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line DC = 5.1cm<\/p>\n\n\n\n

Step 2- Construct and angle of 120o<\/sup> at C.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 6.8cm with C as the center to mark that point as B.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 7.7cm with B as the center to mark that point as A.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 3.6cm with D as the center to intersect at point A.<\/p>\n\n\n\n

Step 6- Now join CB, BA and DA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

4. Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = CD = 5 cm and \u2220B = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = BC = 3 cm, AD = CD = 5 cm and \u2220B = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 3cm<\/p>\n\n\n\n

Step 2- Construct and angle of 120o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 5cm with C as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 5cm with A as the center to intersect at point D.<\/p>\n\n\n\n

Step 6- Now join BC, CD and DA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

5. Construct a quadrilateral ABCD in which AB = 2.8 cm, BC = 3.1 cm, CD = 2.6 cm and DA = 3.3 cm and \u2220A = 60\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 2.8 cm, BC = 3.1 cm, CD = 2.6 cm and DA = 3.3 cm and \u2220A = 60\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 2.8cm<\/p>\n\n\n\n

Step 2- Construct and angle of 60o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3.3cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 2.6cm with D as the center to mark that point as C.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 3.1cm with B as the center to intersect at point C.<\/p>\n\n\n\n

Step 6- Now join AD, DC and CB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

6. Construct a quadrilateral ABCD in which AB = BC = 6 cm, AD = DC = 4.5 cm and \u2220B = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = BC = 6 cm, AD = DC = 4.5 cm and \u2220B = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 6cm<\/p>\n\n\n\n

Step 2- Construct and angle of 120o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 6cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Here, AC is about 10.3cm in length which is greater than AD + CD = 4.5+4.5=9cm<\/p>\n\n\n\n

We know that sum of the two sides of a triangle is always greater than the third side.<\/p>\n\n\n\n

AD + CD < AC<\/p>\n\n\n\n

\u2234 Construction is not possible.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\n\n\n\n

EXERCISE 18.4 PAGE NO: 18.10<\/p>\n\n\n\n

1. Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4 cm, CD = 4 cm, \u2220B = 95\u00b0 and \u2220C = 90\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 6 cm, BC = 4 cm, CD = 4 cm, \u2220B = 95\u00b0 and \u2220C = 90\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line BC = 4cm<\/p>\n\n\n\n

Step 2- Construct and angle of 95o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 6cm with B as the center to mark that point as A.<\/p>\n\n\n\n

Step 4- Construct and angle of 90o<\/sup> at C.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4cm with C as the center to mark that point as D.<\/p>\n\n\n\n

Step 6- Now join BA, CD and AD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2. Construct a quadrilateral ABCD where AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, \u2220B = 30\u00b0 and \u2220C = 150\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, \u2220B = 30\u00b0 and \u2220C = 150\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line BC = 3.6cm<\/p>\n\n\n\n

Step 2- Construct and angle of 30o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 4.2cm with B as the center to mark that point as A.<\/p>\n\n\n\n

Step 4- Construct and angle of 150o<\/sup> at C.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4.8cm with C as the center to mark that point as D.<\/p>\n\n\n\n

Step 6- Now join BA, CD and AD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, \u2220Q = 75\u00b0 and \u2220R = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, \u2220Q = 75\u00b0 and \u2220R = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line QR = 2.5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 75o<\/sup> at Q.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3.5cm with Q as the center to mark that point as P.<\/p>\n\n\n\n

Step 4- Construct and angle of 120o<\/sup> at R.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4.1cm with R as the center to mark that point as S.<\/p>\n\n\n\n

Step 6- Now join QP, RS and PS<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

4. Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm \u2220D = 100\u00b0 and \u2220C = 95<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm \u2220D = 100\u00b0 and \u2220C = 95<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line DC = 4.4cm<\/p>\n\n\n\n

Step 2- Construct and angle of 100o<\/sup> at D.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 5.6cm with D as the center to mark that point as A.<\/p>\n\n\n\n

Step 4- Construct and angle of 95o<\/sup> at C.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 6.6cm with C as the center to mark that point as B.<\/p>\n\n\n\n

Step 6- Now join DA, CB and AB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

5. Construct a quadrilateral ABCD in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, \u2220A = 125\u00b0 and \u2220B = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, \u2220A = 125\u00b0 and \u2220B = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 4.4cm<\/p>\n\n\n\n

Step 2- Construct and angle of 125o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 3.5cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 4- Construct and angle of 120o<\/sup> at B.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 4.7cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 6- Now join AD, BC and CD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

6. Construct a quadrilateral PQRS in which \u2220Q = 45\u00b0 and \u2220R = 90\u00b0, QR = 5 cm, PQ = 9 cm and RS = 7 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are \u2220Q = 45\u00b0 and \u2220R = 90\u00b0, QR = 5 cm, PQ = 9 cm and RS = 7 cm.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line QR = 5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 45o<\/sup> at Q.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 9cm with Q as the center to mark that point as P.<\/p>\n\n\n\n

Step 4- Construct and angle of 90o<\/sup> at R.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 7cm with R as the center to mark that point as S.<\/p>\n\n\n\n

Step 6- Now join QP, RS<\/p>\n\n\n\n

Since the line segment QP and RS are not intersecting at each other, quadrilateral cannot be formed.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

7. Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = 5 cm, \u2220A = 90\u00b0 and \u2220B = 105\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = BC = 3 cm, AD = 5 cm, \u2220A = 90\u00b0 and \u2220B = 105\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 3cm<\/p>\n\n\n\n

Step 2- Construct and angle of 90o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 5cm with A as the center to mark that point as D.<\/p>\n\n\n\n

Step 4- Construct and angle of 105o<\/sup> at B.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 3cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 6- Now join AD, BC and CD<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

8. Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, \u2220F = 50\u00b0 and \u2220E = 100\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, \u2220F = 50\u00b0 and \u2220E = 100\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line EF = 3.5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 100o<\/sup> at E.<\/p>\n\n\n\n

Step 3- Cut an arc of radius 4.5cm with E as the center to mark that point as D.<\/p>\n\n\n\n

Step 4- Construct and angle of 50o<\/sup> at F.<\/p>\n\n\n\n

Step 5- Cut an arc of radius 6.5cm with F as the center to mark that point as B.<\/p>\n\n\n\n

Step 6- Now join DE, FB and DB<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\n\n\n\n

EXERCISE 18.5 PAGE NO: 18.13<\/p>\n\n\n\n

1. Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, \u2220A = 75\u00b0, \u2220B = 80\u00b0 and \u2220C = 120\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 4 cm, BC = 3 cm, \u2220A = 75\u00b0, \u2220B = 80\u00b0 and \u2220C = 120\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 4cm<\/p>\n\n\n\n

Step 2- Construct and angle of 75o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Construct and angle of 80o<\/sup> at B.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 5- Construct and angle of 120o<\/sup> at C such that it meets the line segment AX, mark that point as D.<\/p>\n\n\n\n

Step 6- Now join BC, CD and DA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2. Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 3.7 cm, \u2220A = 60\u00b0, \u2220B = 105\u00b0 and \u2220D = 90\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are AB = 5.5 cm, BC = 3.7 cm, \u2220A = 60\u00b0, \u2220B = 105\u00b0 and \u2220D = 90\u00b0.<\/p>\n\n\n\n

We know that \u2220A + \u2220B + \u2220C + \u2220D = 360o<\/sup><\/p>\n\n\n\n

\u2234 \u2220C = 105o<\/sup><\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line AB = 5.5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 60o<\/sup> at A.<\/p>\n\n\n\n

Step 3- Construct and angle of 105o<\/sup> at B.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C.<\/p>\n\n\n\n

Step 5- Construct and angle of 105o<\/sup> at C such that it meets the line segment AX, mark that point as D.<\/p>\n\n\n\n

Step 6- Now join BC, CD and DA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, \u2220P = \u2220R = 105\u00b0 and \u2220S = 75\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are PQ = 3.5 cm, QR = 6.5 cm, \u2220P = \u2220R = 105\u00b0 and \u2220S = 75\u00b0.<\/p>\n\n\n\n

We know that \u2220P + \u2220Q + \u2220R + \u2220S = 360o<\/sup><\/p>\n\n\n\n

\u2234 \u2220Q = 75o<\/sup><\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line PQ = 3.5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 105o<\/sup> at P.<\/p>\n\n\n\n

Step 3- Construct and angle of 75o<\/sup> at Q.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R.<\/p>\n\n\n\n

Step 5- Construct and angle of 105o<\/sup> at R such that it meets the line segment PX, mark that point as S.<\/p>\n\n\n\n

Step 6- Now join QR, RS and PS<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

4. Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, \u2220A = 70\u00b0, \u2220B = 110\u00b0 and \u2220D = 85\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are BC = 5.5 cm, CD = 4.1 cm, \u2220A = 70\u00b0, \u2220B = 110\u00b0 and \u2220D = 85\u00b0.<\/p>\n\n\n\n

We know that \u2220A + \u2220B + \u2220C + \u2220D = 360o<\/sup><\/p>\n\n\n\n

\u2234 \u2220C = 95o<\/sup><\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line BC = 5.5cm<\/p>\n\n\n\n

Step 2- Construct and angle of 110o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Construct and angle of 95o<\/sup> at C.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Construct and angle of 85o<\/sup> at D such that it meets the line segment BX, mark that point as A.<\/p>\n\n\n\n

Step 6- Now join CD, DA and BA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

5. Construct a quadrilateral ABCD \u2220A = 65\u00b0, \u2220B = 105\u00b0, \u2220C = 75\u00b0, BC = 5.7 cm and CD = 6.8 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are \u2220A = 65\u00b0, \u2220B = 105\u00b0, \u2220C = 75\u00b0, BC = 5.7 cm and CD = 6.8 cm.<\/p>\n\n\n\n

We know that \u2220A + \u2220B + \u2220C + \u2220D = 360o<\/sup><\/p>\n\n\n\n

\u2234 \u2220D = 115o<\/sup><\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line BC = 5.7cm<\/p>\n\n\n\n

Step 2- Construct and angle of 105o<\/sup> at B.<\/p>\n\n\n\n

Step 3- Construct and angle of 75o<\/sup> at C.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 6.8cm with C as the center to mark that point as D.<\/p>\n\n\n\n

Step 5- Construct and angle of 115o<\/sup> at D such that it meets the line segment BX, mark that point as A.<\/p>\n\n\n\n

Step 6- Now join CD, DA and BA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

6. Construct a quadrilateral PQRS in which PQ = 4 cm, QR = 5 cm \u2220P = 50\u00b0, \u2220Q = 110\u00b0 and \u2220R = 70\u00b0.<\/strong><\/p>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

The given details are PQ = 4 cm, QR = 5 cm \u2220P = 50\u00b0, \u2220Q = 110\u00b0 and \u2220R = 70\u00b0.<\/p>\n\n\n\n

Steps to construct a quadrilateral:<\/p>\n\n\n\n

Step 1- Draw a line PQ = 4cm<\/p>\n\n\n\n

Step 2- Construct and angle of 50o<\/sup> at P.<\/p>\n\n\n\n

Step 3- Construct and angle of 110o<\/sup> at Q.<\/p>\n\n\n\n

Step 4- Cut an arc of radius 5cm with Q as the center to mark that point as R.<\/p>\n\n\n\n

Step 5- Construct and angle of 70o<\/sup> at R such that it meets the line segment PX, mark that point as S.<\/p>\n\n\n\n

Step 6- Now join QR, RS and PS<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

RD Sharma Solutions for Class 8 Maths Chapter 18: Download PDF<\/strong><\/h2>\n\n\n\n

RD Sharma Solutions for Class 8 Maths Chapter 18\u2013Practical Geometry (Constructions)<\/p>\n\n\n\n

Download PDF<\/strong>: RD Sharma Solutions for Class 8 Maths Chapter 18\u2013Practical Geometry (Constructions) PDF<\/a><\/p>\n\n\n\n

Chapterwise RD Sharma Solutions for Class 8 Maths :<\/strong><\/h2>\n\n\n\n