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CBSE Class 9 Mathematics Worksheet

Unit 4-Geometry - Construction

1.

State True/False:  A can be constructed in which AC = 10 cm, and BC = 7 cm, AB =6 cm.

A) True B) False
2.

Construct a triangle ABC in which BC = 6 cm, and .

3.

State True/False:  To construct a triangle given its base, a base angle and the sum of the other two sides is required.

A) True B) False
4.

Construct a rhombus whose side is of length 4 cm and one of its angles is .

5.

Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm.

6.

A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm.

7.

Construct a square of side 4 cm.

8.

State True/False:  An angle of can be constructed with the help of a ruler or compass.

A) True B) False
9.

Construct a rectangle whose adjacent sides are of lengths 6 cm and 4.5 cm and one of its adjacent angle is .

10.

Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18 cm.

11.

Construct a triangle ABC  in which, ∠B = , ∠C = and its perimeter is 12 cm.

12.

Draw an angle of 85° with the help of a protractor and bisect it.

13.

State True/False:  To construct a triangle given its base, a base angle and the sum of the other two sides is required.

A) True B) False
14.

State True/False:  An angle of can be constructed with the help of a ruler or compass.

A) True B) False
15.

Choose the correct option:

The construction of a , given that PQ = 7 cm, is not possible when sum of PR and QR is equal to _______.

A) 13 cm B) 12 cm C) 6.5 cm D) 15 cm
16.

Construct an equilateral triangle if its side is 6 cm.

17.

Construct a triangle XYZ in which YZ = 6 cm, ∠Y = 60° and XZ + XY = 8 cm.

18.

Choose the correct option:  

The construction of a , given that BC = 5 cm, is possible when difference of AB and AC is equal to ________.

A) 5.6 cm B) 4.6 cm C) 5.5 cm D) 6.2 cm
19.

Construct an angle bisector of an angle of

20.

Choose the correct option:  

With the help of a ruler and a compass, it is possible to construct an angle of ________.

A) 50 degree B) 40 degree C) 21.5 degree D) 22.5 degree

CBSE Class 9 Mathematics Worksheet

Unit 4-Geometry - Construction

Answers

1.
Option B

2.

To be constructed

Solution:

Steps of construction:

1). Draw a line segment BC = 6 cm.

2). Draw  and .

3). Get the intersection point A on BY and CP.

ABC is the rquired triangle.

3.
Option B

4.

To be constructed.

Solution:

Steps to construction:

1). Draw a line segment AB = 4 cm.

2). At A, draw an angle PAB =

3). With A as centre draw an arc of radius 4 cm, to intersect X AX at D.

4). With D and B as centre, draw arcs of radius 4 cm to intersect each other at C.

5). Join CD and BC

ABCD is the required rhombus.

5.

To be constructed

Solution:

Steps of construction:

1). Draw a line segment AB of length = 5 cm.

2). At B draw angle B = 90.

3). With B as center and radius = 3.5 cm, draw an arc, cutting BE at C.

4). With A as center and radius = 3.5 cm, draw an arc.

5). With C as centre and radius = 5 cm, draw another arc cutting the previous arc at D.

6). Join AD and CD.

ABCD is the required rectangle.

 

6.

To be constructed

Solution:

Steps to construction:

1). Draw a ray BX and cut off a line segment BC = 3.5 cm. 

2). Construct angle B = 

3). From BY cut off line segment BD = 5.5 cm.

4). Join CD.

5). Draw the perpendicular bisector of CD, intersecting BD at point A.

6). Join AC

ABC is a required triangle.

7.

To be constructed

Solution:

Steps to construction:

1). Draw a line segment AB = 4 cm.

2). With B as centre, draw an angle of

3). With B as centre and radius = 4 cm, cut an arc on C.

4). With A as centre and radius = 4 cm, draw an arc.

5). With C as centre and radius = 4 cm, draw an arc intersecting the previous arc at D.

6). Join AD and CD.

ABCD is the required square.

8.
Option B

9.

To be constructed

10.

To be constructed

Solution:

Steps of construction:

1).  Draw a line segment BC = 12 cm.

2). Draw an

3). Cut off a line segment BD = 18 cm.

4). Join CD

5). Draw the perpendicular bisector of CD, intersecting BD at a point A.

6). Join AC.

ABC is the required triangle.

11.

To be constructed

Solution:

Steps of construction:

1). Draw a line segment XY = 12 cm.

2). With X as centre, draw angle X =  and with Y as centre draw angle Y = .

3). Draw angle bisectors on X and Y intersecting at A.

4). Draw line bisector of XA and AY respectively. Name the intersecting points on XY as B and C.

5). Join AB and AC.

ABC is the required triangle

12.

To be constructed

13.
Option A
14.
Option A
15.
Option C

16.

Solution:

Steps of construction:

1). Draw a line PQ.

2). Take any point L on this line.

3). Construct perpendicular AL on PQ.

4). Cut a line segment AD from D equal to 6 cm.

5). Make angles equal to 30 degree at A on both sides of AD.

Then, ABC is a required triangle.

17.

To be constructed

 

Solution:

Steps to construction:

1). Draw a line segment YZ = 6 cm.

2). Draw angle Y =

3). With Center Y and radius 8 cm, make an arc which intersects YA at B.

4). Join B to X.

5). Draw a perpendicular bisector of segment BX intersecting the line segment BY at point Z.

6). Join Z to X.

XYZ is the required triangle.

18.
Option B

19.

To be constructed

20.
Option D

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