NCERT Exemplar Class 9 Maths: Chapter-11

NCERT Exemplar Class 9 Maths
CHAPTER- 11
Sample Question 1: With the help of a ruler and a

compass, it is possible to
construct an angle of :
(A) 35° (B) 40° (C) 37.5° (D) 47.5°
Solution : Answer (C)
Sample Question 2: The construction of a triangle ABC

in which AB = 4 cm,
ÐA = 60° is not possible when difference of BC and AC

is equal to:
(A) 3.5 cm (B) 4.5 cm
(C) 3 cm (D) 2.5 cm
Solution : Answer (B)
EXERCISE 11.1
1. With the help of a ruler and a compass it is not

possible to construct an angle of :
(A) 37.5° (B) 40° (C) 22.5° (D) 67.5°
1
Solution-
(B) 400.
2. The construction of a triangle ABC, given that BC =

6 cm, ÐB = 45° is not possible when difference of AB
and AC is equal to:
(A) 6.9 cm (B) 5.2 cm
(C) 5.0 cm (D)4.0 cm
Solution-
(A) 6.9 cm !difference of any two sides of a D is less

than third side.
3. The construction of a triangle ABC, given that BC =

3 cm, ÐC = 60° is possible when difference of AB and
AC is equal to :
(A) 3.2 cm (B) 3.1 cm
(C) 3 cm (D) 2.8 cm
Solution-
(D) 2.8 cm
2
!difference of any two sides of a D is less than third

side.
EXERCISE 11.2
Write True or False in each of the following. Give

reasons for your answer:
1. An angle of 52.5° can be constructed.
Solution-
True : by bisecting angle of 1050.
2. An angle of 42.5° can be constructed.
Solution-
False : ! 42.5 ´ 2 = 850 angle cannot be constructed.
3. A triangle ABC can be constructed in which AB = 5

cm, ÐA = 45° and BC +
AC = 5 cm.
Solution :
False : ! BC + AC ¹ AB
3
4. A triangle ABC can be constructed in which BC = 6

cm, ÐC = 30° and AC – AB = 4 cm.
Solution –
True : ! AC - AB < BC
5. A triangle ABC can be constructed in which ÐB =

105°, ÐC = 90° and AB + BC + AC = 10 cm.
Solution –
False : ! ÐB + ÐC = 195which is greater than 1800 which is

sum of 3 interior Ð& of a D.
6. A triangle ABC can be constructed in which ÐB =

60°, ÐC = 45° and AB + BC + AC = 12 cm.
Solution-
True : ! ÐB + ÐC = 60 + 45 = 1050 < 1800
EXERCISE 11.3
1. Draw an angle of 110° with the help of a protractor

and bisect it. Measure each angle.
Solution-
4
Steps :
1. draw ÐAOB = 1100
2. with center O and any radius draw an or NM.
3. with center M and N are equal radius draw are &

inter each other at P.
4. Join OP.
2. Draw a line segment AB of 4 cm in length. Draw a

line perpendicular to AB through A and B, respectively.
Are these lines parallel?
Solution-
5
Yes XX' ! YY '
Steps –
1. draw AB= 4 cm
2. draw XAX ' ^ AB
3. draw YAY ' ^ AB
3. Draw an angle of 80° with the help of a protractor.

Then construct angles of
(i) 40° (ii)160° and (iii) 120°.
Solution-
6
7
Steps :
1. draw ÐAOB = 800
2. with any radius and center O, draw are XY.
3. with center X and Y and any radius draw arcs

intersecting each other at C
4. ÐCOB = 400
5. with centers Y and P draw arcs with equal radius

intersecting each other at D.
6. ÐDOB = 600
7. with center Q and r = XQ draw an arc intersecting

arc XQ produced at R.
8. ÐEOF = 1200
8
4. Construct a triangle whose sides are 3.6 cm, 3.0 cm

and 4.8 cm. Bisect the smallest angle and measure
each part.
Solution-
ÐABZ = ÐCBZ = 200

Here ÐABC is smallest
! it is opposite to smallest side
5. Construct a triangle ABC in which BC = 5 cm, ÐB =

60° and AC + AB = 7.5 cm.
Solution-
9
Steps
1. draw ÐYBX = 600
2. with center B and radii 5 cm and 7.5 cm draw arcs

inter B x, C and B Y at Z.
3. draw PQ per bisects of ZC intersecting B Z at A.
4. Join AC
5. ABC is required D
6. Construct a square of side 3 cm.
Solution-
10
7. Construct a rectangle whose adjacent sides are of

lengths 5 cm and 3.5 cm.
Solution-
Steps –
1. draw AB= 5cm
2. draw ÐABZ = 900
3.with center B and r. = 3.5 cm draw arc intersecting B

Z at C
4. with center A and C and radii 3.5 cm and 5 cm

respectively draw arc inter each other at D
11
5. Join CD and DA
6. ABCD is required rectangle
8. Construct a rhombus whose side is of length 3.4 cm

and one of its angles is 45°.
Steps-
1.draw ÐYBW = 450
2. with center B and radii 3.4 cm each draw arc

intersecting By at C and B W at A respectively.
3. with center A and C and radii 3.4 cm each draw arc

intersecting each other at D
12
4. Join AD and CD
5. ABCD is required rhombus.
EXERCISE 11.4
Construct each of the following and give justification :
1. A triangle if its perimeter is 10.4 cm and two angles

are 45° and 120°.
Solution-
2. A triangle PQR given that QR = 3cm, Ð PQR = 45°

and QP – PR = 2 cm.
Solution-
13
Steps-
1. draw ÐYQZ = 450
2. with center Q and radii 3 cm and 2 cm respectively

draw arcs intersecting QZ at R and QY at C
3. Join CR and draw AB its perpendicular bisects, QY

and BA produced inter. Each other at P.
4. PQR is required D
3. A right triangle when one side is 3.5 cm and sum of

other sides and the hypotenuse is 5.5 cm.
Solution-
14
Steps-
1. draw ÐYBX = 900
2. with center B and radii 3.5 cm and 5.5 cm

respectively draw arcs intersecting BX at C and BY at
Z.
3. Join ZC and draw its perpendicular bisector

intersecting BY at A.
4. Join AC
4. An equilateral triangle if its altitude is 3.2 cm.
Solution-
Steps
15
1. draw line XY
2. take a point D on XY and DZ ^ XY
3. with center D and radii 3.2 cm draw an arc

intersecting DZ at A.
4. draw ÐUAD = 300 intersecting XY at B and ÐVAD = 300 inter

XY at C.
5. A rhombus whose diagonals are 4 cm and 6 cm in

lengths.
16
Steps
1. draw AC= 6 cm
2. draw PQ perpendicular bisector of AC intersecting it

at O.
3. with center O and radii ½ BD or 2 cm each draw

arcs intersecting OP at D and OQ at B
4. join AB, BC, CD and DA
17

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NCERT Exemplar Class 9 Maths

Sample Question 1: With the help of a ruler and a

(A) 35° (B) 40° (C) 37.5° (D) 47.5°

Solution : Answer (C)

Sample Question 2: The construction of a triangle ABC

ÐA = 60° is not possible when difference of BC and AC

(A) 3.5 cm (B) 4.5 cm

(C) 3 cm (D) 2.5 cm

Solution : Answer (B)

1. With the help of a ruler and a compass it is not

(A) 37.5° (B) 40° (C) 22.5° (D) 67.5°

2. The construction of a triangle ABC, given that BC =

(A) 6.9 cm (B) 5.2 cm

(C) 5.0 cm (D)4.0 cm

(A) 6.9 cm !difference of any two sides of a D is less

3. The construction of a triangle ABC, given that BC =

(A) 3.2 cm (B) 3.1 cm

(C) 3 cm (D) 2.8 cm

!difference of any two sides of a D is less than third

Write True or False in each of the following. Give

1. An angle of 52.5° can be constructed.

True : by bisecting angle of 1050.

2. An angle of 42.5° can be constructed.

False : ! 42.5 ´ 2 = 850 angle cannot be constructed.

3. A triangle ABC can be constructed in which AB = 5

4. A triangle ABC can be constructed in which BC = 6

5. A triangle ABC can be constructed in which ÐB =

False : ! ÐB + ÐC = 195which is greater than 1800 which is

6. A triangle ABC can be constructed in which ÐB =

True : ! ÐB + ÐC = 60 + 45 = 1050 < 1800

1. Draw an angle of 110° with the help of a protractor

1. draw ÐAOB = 1100

2. with center O and any radius draw an or NM.

3. with center M and N are equal radius draw are &

2. Draw a line segment AB of 4 cm in length. Draw a

Yes XX' ! YY '

2. draw XAX ' ^ AB

3. draw YAY ' ^ AB

3. Draw an angle of 80° with the help of a protractor.

(i) 40° (ii)160° and (iii) 120°.

1. draw ÐAOB = 800

2. with any radius and center O, draw are XY.

3. with center X and Y and any radius draw arcs

5. with centers Y and P draw arcs with equal radius

7. with center Q and r = XQ draw an arc intersecting

4. Construct a triangle whose sides are 3.6 cm, 3.0 cm

ÐABZ = ÐCBZ = 200

5. Construct a triangle ABC in which BC = 5 cm, ÐB =

1. draw ÐYBX = 600

2. with center B and radii 5 cm and 7.5 cm draw arcs

3. draw PQ per bisects of ZC intersecting B Z at A.

6. Construct a square of side 3 cm.

7. Construct a rectangle whose adjacent sides are of

1. draw AB= 5cm

2. draw ÐABZ = 900

3.with center B and r. = 3.5 cm draw arc intersecting B

4. with center A and C and radii 3.5 cm and 5 cm

6. ABCD is required rectangle