AP 9th Maths Mock Test 2021 For Chapter - 13 : "Geometrical Constructions" Online Practice Test

1. The construction of a $\bigtriangleup$ ABC in which AB = 8 cm , $\angle$ A = 45⁰ is possible when (BC + AC) is

7 cm

9 cm

5 cm

6 cm

2. The construction of a $\triangle$ PQR in which PQ = 7 cm $\angle$ P = 75⁰ is possible when (QR - PR) is.............

6 cm

7 cm

6.5 cm

8 cm

3. The construction of a $\triangle$ ABC in which BC = 6.4 cm $\angle$ B = 60⁰ is not possible when (AB + AC) is.............

6 cm

7 cm

6.5 cm

8 cm

4. The process of drawing geometrical figure by using a compass and ungraduated ruler is called ...........

Hypothesis

Figure

Geometrical proof

Geometrical construction

5. In a right angle triangle , one angle is 30⁰ then the other angle is

45⁰

30⁰

50⁰

60⁰

6. The construction of triangle ABC in which BC = 6 cm , $\angle$ B = 45⁰ is not possible when difference of AB and AC is equal

6.9 cm

5.2 cm

5.0 cm

4.5 cm

7. The construction of triangle ABC in which AB = 4 cm , $\angle$ A = 60⁰ is not possible when difference of BC and AC is equal to

3.5 cm

4.5 cm

3 cm

2.5 cm

8. The construction of triangle ABC , given that BC = 3 cm , $\angle$ C = 60⁰ is possible when difference of AB and AC is equal to

3.2 cm

3.1 cm

3 cm

2.8 cm

9. The construction of $\triangle$ DEF , given that DE = 7 cm , $\angle$ D = 75⁰ is possible when (EF - DF) is equal to

7.5 cm

7 cm

8 cm

6.5 cm

10. To construct an angle , we start with ray $\overrightarrow{OP}$ and with a radius cut OP at A and keeping the same radius . Starting from A mark Q , R and S on the previous are such that AQ = QR = RS . Now draw bisector OL and OM of RS and RL respectively then $\angle$ POM = ..............

45⁰

60⁰

90⁰

135⁰

11. The construction of $\triangle$ ABC in which AB = 5 cm , $\angle$ A = 75⁰ is possible when (BC - AC) is equal to

5 cm

5.2 cm

4.5 cm

6 cm

12. Which of the following angles can be constructed by using ruler and compass only

72⁰

130⁰

105⁰

20⁰

13. Which of the following angles can not be constructed by using ruler and compass only

70⁰

90⁰

45⁰

All

14. In a triangle PQR , PQ + QR is .............PR

Can't say

15. Among the angles 22 $\frac{1}{2}^{0}$ , 67 $\frac{1}{2}^{0}$ , 82 $\frac{1}{2}^{0}$ , 102 $\frac{1}{2}^{0}$ only which angle can not be constructed by using ruler and compass

22 $\frac{1}{2}^{0}$

67 $\frac{1}{2}^{0}$

82 $\frac{1}{2}^{0}$

102 $\frac{1}{2}^{0}$

16. Among the angles 25⁰ , 35⁰ , 45⁰ , 55⁰ only ...................... can be constructed by using ruler and compass

55⁰

45⁰

35⁰

25⁰

17. In a triangle ABC , AB - BC is ..................

None

18. Let AB be a line segment and PQ be the perpendicular bisector of AB which cuts at M then which of the following are true ?

AM = BM

AP = PB

$\angle$ AMP = $\angle$ PMB = 90⁰

All

19. The angle in the semicircle is ..............

30⁰

45⁰

60⁰

90⁰

20. In a right angled triangle ABC with $\angle$ B = 90⁰ , which of the following are true ?

$\angle$ A + $\angle$ C = 90⁰
AC > Ab or BC
AB = BC

Only 1

1 , 2

2 , 3

All

21. In a triangle if two angles are acute then the angle is

Acute

Right

Obtuse

Any one of them

22. Let P be a point on a perpendicular bisector of a line segment $\overline{AB}$ then

P is equidistant from A , B

P lies on AB

PA : PB = 1 : 2

PA : PB = 2 : 3

23. Which of the following angles cannot be constructed using ruler and compass only ?

15⁰

75⁰

22 $\frac{1}{2} ^{0}$

32 $\frac{1}{2} ^{0}$

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

37.5⁰

40⁰

47.5⁰

35⁰

25. With the help of of a ruler and a compass , it is not possible to construct an angle of ...............

37.5⁰

40⁰

47.5⁰

35⁰

26. Which of the following statements are true ?

We can construct 120⁰ using only ruler and compass

We can construct 22 $\frac{1}{2} ^{0}$ using only ruler and compass

Both

None

27. If a , b , c are lengths of a triangle ABC then to construct the triangle we must have..................
(I) a + b > c (II) a - b < c
b + c > a b - c < a
a + c > b a - c < b

Only I

Only II

Either I or II

Neither I nor II

28. If perimeter of a triangle is given then to construct the triangle , we need

Base angle and length of base

Length of two sides

Two base angles

Nothing

29. If base and one of the base angle is given , then what is the third condition required to construct a triangle

Sum of other two sides
Sum of other two angles
Differences of other two angles
Difference of other two sides

Only 1

2 , 3

1 , 3

All

30. Which of the following conditions are sufficient to construct a triangle ?

Length of base , base angle and sum of other two sides

Length of base , base angle and differences of other two sides

Perimeter and two base angles

All

31. Observe the steps of the following

With P as centre and radius (> $\frac{1}{2}$ PQ) draw an arc
Given an angle BAC
With A as centre with many radius , draw an arc , cutting $\overline{AB}$ , $\overline{AC}$ at P and Q respectively
Join AR and produce to obtain ray $\overrightarrow{AX}$
With Q as centre and with same radius , draw another arc cutting the previous arc at R

Put the steps in order to construct a bisector of $\angle$ BAC

1 , 2 , 3 , 4 , 5

2 , 3 , 1 , 5 , 4

2 , 1 , 3 , 5 , 4

3 , 2 , 1 , 4 , 5

32. A perpendicular bisector of a given line segment LM can be constructed using following steps given without order , put them in an order

Join RS intersecting LM at P , then P bisects the line segment LM
Let these arcs intersect each other at R and S
Taking L and M on centres and radius more than $\frac{1}{2}$ LM , draw arcs on both sides of the of the line segment LM
Join LR , RM MS and LS

1 , 3 , 2 , 4

3 , 2 , 4 , 1

3 , 2 , 1 , 4

4 , 1 , 3 , 2

33. Put the following steps in order to construct an angle 60⁰ at 'O' of a given ray $\overrightarrow{OA}$

With centre O and any radius , draw an arc PQ cutting the ray OA at P
Join OR an d produce it to obtain a ray $\overrightarrow{OB}$
Draw a ray $\overrightarrow{OA}$
With centre P and the same radius as above , draw an arc cutting the arc PQ at R
$\angle$ AOB so obtained is the angle of measure 60⁰

3 , 1 , 4 , 2 , 5

3 , 4 , 2 , 1 , 5

2 , 3 , 1 , 4 , 5

5 , 1 , 3 , 2 , 4

34. In the figure , if XY is perpendicular bisector of PQ then PX = ......

35. In the figure , if XY is perpendicular bisector of PQ then triangle PXQ is .................... triangle

Isosceles

Scalene

Right

Equilateral

36. In the figure , if XY is perpendicular bisector of PQ then triangle PXO =

Triangle PYO

Triangle QYO

Triangle PXQ

Triangle QXO

37. Arrange the following steps of construction of a triangle ABC in which BC = 8 cm , $\angle$ B = 30⁰ and Ab + Ac = 2 cm in order

PQ intersects BD at A and CD at L
Join CD
Draw BC = 8 cm
Construct $\angle$ CBX = 30⁰
Draw PQ , the perpendicular bisector of CD
Join CA
Along BX , cut BD = 12 cm

3 , 4 , 7 , 2 , 5 ,1 , 6

3 , 4 , 2 , 5 , 1 , 7 , 6

3 , 4 , 2 , 7 , 1 , 5 , 4

1 , 2 , 3 , 7 , 6 , 4 , 5

38. We have to construct a $\triangle$ ABC such that BC = 6 cm , $\angle$ B = 45⁰ and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and $\angle$ CBX = 45⁰
From the data , in the next step of construction we produce XB to D so that

BD = 4 cm

BD = 6 cm

BD = 3 cm

BD = 2 cm

39. We have to construct a $\triangle$ ABC such that BC = 6 cm , $\angle$ B = 45⁰ and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and $\angle$ CBX = 45⁰
From the data , next we join CD and draw PQ which is ............. of CD

Angular bisector

Median

Perpendicular bisector

Only bisector

40. We have to construct a $\triangle$ ABC such that BC = 6 cm , $\angle$ B = 45⁰ and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and $\angle$ CBX = 45⁰
From the data , Let PQ intersects BX at A and CD at L then what is next step ?

Join AB

Join BC

Join AC

Join XA

41. In the figure XY perpendicular to AB then Ax =

42. In the figure triangle AXB is

Equilateral

Scalene

Isosceles

Right angled

43. In the figure $\triangle$ AXO $\cong$ =

$\triangle$ BXO

$\triangle$ BYO

$\triangle$ AXB

$\triangle$ AYO

44. In the figure $\overrightarrow{BD}$ is the bisector of $\angle$ ABC then

$\angle$ ABD = $\angle$ CBD

$\angle$ ABD = $\angle$ ABC

$\angle$ ABD + $\angle$ CBD = 90⁰

$\angle$ ABD + $\angle$ CBD = 180⁰

45. If in $\triangle$ ABC , $\overrightarrow{BX}$ and $\overrightarrow{CY}$ are bisectors to the base then $\angle$ BXC =

90⁰ - $\frac{1}{2} \angle$ A

90⁰ + $\frac{1}{2} \angle$ A

180⁰ - $\frac{1}{2} \angle$ A

180⁰ + $\frac{1}{2} \angle$ A

46. Arrange the following steps in order if we construct a bisector of a line segment

Draw a line segment
Join EF intersecting AB at M , then M bisects the line segment AB as shown in figure
With centre A and radius more than half of AB , draw arcs , one on each sides of AB
With B as centre and the same radius as before , draw arcs , cutting the previously drawn arcs at E and F respectively

1 , 2 , 3 , 4

1 , 3 , 4 , 2

1 , 3 , 2 , 4

1 , 2 , 4 , 3

47. To construct an angle bisector , arrange the following steps in order

Join AR and produce it to any point X . the ray AX is the required bisector of $\angle$ BAC
With centre Q and the same radius draw another arc intersecting previous arc
With centre 'P' and radius more than $\frac{1}{2}$ PQ draw an arc
With centre A and any convenient radius draw an arc cutting AB and AC at P and Q respectively

1 ,2 , 3 , 4

2 , 3 , 4 , 1

3 , 4 , 1 , 2

4 , 3 , 2 , 1

48. To construct a circle segment given a

Chord , Angle

Angle only

Chord only

Two base angles

49. To construct a triangle , we need

Perimeter

Two base angles

Both

Chord

50. To construct a triangle we need

Its base , base angle and sum of other two sides

Its base , base angle and difference of other two sides

Its perimeter and an angle

All

51. A geometrical construction is the process of drawing geometrical figures by using ......... instruments

52. A geometrical construction is the process of drawing geometrical figures using instruments are

Ungraduated ruler and compass

Ungraduated ruler

Compass only

None

53. The box containing a graduated ruler , a pair of set squares , a divider , a compass and a protractor is called

Geometry box

Constructional box

Both

None

54. Each angle of an equilateral triangle is

60⁰

70⁰

80⁰

90⁰

55. The angle in a semicircle is

60⁰

70⁰

80⁰

90⁰

56. Draw a circle , identify a point on it . Cut arcs on the circle with the length of the radius in succession , how many arts can the circle be divided into ?

57. Construct a segment of a circle on a chord of length 5 cm . containing the angle 90⁰

Draw a line segment $\overline{AB}$ = 5 cm
Mark any point 'C' on the semi - circle and join AC and AB to form $\angle$ ACB = 90⁰
Taking OA or OB as radius with centre 'O' draw a semi circle
Draw the perpendicular bisector of AB to cut at 'O'

1 , 4 , 3 , 2

1 , 2 , 3 , 4

4 , 3 , 2 , 1

1 , 4 , 2 , 3

58. Construct a segment of a circle on a chord of length 5 cm . containing the angle 45⁰

Draw two rays $\overrightarrow{AX}$ , $\overrightarrow{BY}$ at A , B such that they meet at 'O'
Mark the point 'C' such that
Taking OA or OB as radius with centre 'O' draw a circle
Draw a line segment AB = 5 cm

4 , 1 , 3 , 2

1 , 2 , 3 , 4

4 , 3 , 2 , 1

1 , 4 , 2 , 3

59. Construct a segment of a circle on a chord of length 5 cm . containing the angle 120⁰

Mark the point 'C' on AZB sector . $\angle$ ACB = 120⁰
Taking 'O' as centre and with OA or OB as radius draw a circle
Draw $\overrightarrow{AX}$ , $\overrightarrow{BY}$ rays such that they meet at 'O' . So $\angle$ BAX = $\angle$ ABY = 30⁰
Draw a line segment AB = 5 cm

4 , 1 , 3 , 2

1 , 2 , 3 , 4

4 , 3 , 1 , 2

4 , 3 , 2 , 1

60. Construct a right angled triangle whose base is 7.5 cm and sum of its hypotenuse and other side is 15 cm

Draw the base BC = 7.5 cm and construct $\angle$ CBX = 90⁰ at B
Taking B as centre and radius as 15 cm ( = AB + AC ) , draw an arc to meet $\overrightarrow{BX}$ at D
Join $\overline{CD}$ and draw the perpendicular bisector of CD ,let it be met $\overrightarrow{BD}$ at A
Join $\overline{AC}$ to form $\triangle$ ABC

1 , 2 , 3 , 4

4 , 3 , 2 , 1

1 , 4 , 2 , 3

4 , 1 , 3 , 2

61. Construct XYZ in which $\angle$ Y = 30⁰ , $\angle$ Z = 60⁰ and XY + YZ + ZX = 10 cm

Draw line segment AB = 10 cm
Join XY and XZ
Construct $\angle$ BAL= 30⁰ and $\angle$ ABM = 60⁰
Draw perpendicuular bisectors of AX and BX and let them meet the line segment AB at Y and Z respectively
Draw angular bisectors of $\angle$ A and $\angle$ B to meet at X

1 , 5 , 2 , 4 , 3

1 , 3 , 5 , 4 , 2

5 , 1 , 4 , 2 , 3

None

62. Construct $\triangle$ PQR in which QR = 8 cm , $\triangle$ Q = 60⁰ and PQ - PR = 3.5 cm

Join PR to get the required triangle PQR
Draw the perpendicular bisectors of SR and let it meet the ray $\overline{QX}$ at the point 'P'
First construct the triangle QRS using SAS rule with measures QR = 8 cm , QS = 3.5 cm and $\angle$ Q = 60⁰

1 , 2 , 3

3 , 2 , 1

1 , 3 , 2

2 , 3 , 1

63. Construct $\triangle$ ABC in which BC = 7 cm , $\angle$ B = 75⁰ and AB + AC = 12 cm

Join $\overline{AC}$ to get the required triangle
Join CD and draw perpendicular bisector of $\overline{CD}$ to meet $\overline{BD}$ at A
Draw the base BC = 7 cm and construct $\angle$ CBX = 75⁰ at B
With centre B and radius 12 cm(+AB + AC) draw an arc on $\overline{BX}$ to meet at D

2 , 3 , 4 , 1

4 ,3 , 2 , 1

1 , 2 , 3 , 4

3 , 4 , 2 , 1

64. Construct an iscosceles triangle , given its base AB as 5 cm and $\angle$ A = 50⁰

Let the point of intersection of two rays be 'C'
Draw a ray making same angle 50⁰ at B
Draw a ray making same angle 50⁰ at A
Draw a line segment AB of length 5 cm

4 , 3 , 2 , 1

1 , 2 , 3 , 4

2 , 3 , 4 , 1

3 , 4 , 1 , 2

65. Construct an iscosceles triangle , given its base PQ as 10 cm and $\angle$ P = 60⁰

Let the point of intersection of two rays be 'R'
Draw a ray making same angle 60⁰ at Q
Draw a ray making same angle 60⁰ at P
Draw a line segment PQ of length 10 cm

4 , 3 , 2 , 1

1 , 2 , 3 , 4

2 , 3 , 4 , 1

3 , 4 , 1 , 2

66. Write the correct order for construct an equilateral triangle , given its side length 4.5 cm and justify the construction

Draw a line segment AB of any length say 4.5 cm
Taking centres at A and B with radius equal to length of AB i.e, 4.5 cm we draw two arcs to meet at C
Join A , C and B , C

2 ,1 , 3

2 , 3 , 1

3 , 2 , 1

1 , 2 , 3

67. Write the correct order for construct an equilateral triangle , given its side length 5.5 cm and justify the construction

Draw a line segment RS of any length say 4.5 cm
Taking centres at R and S with radius equal to length of AB i.e, 5.5 cm we draw two arcs to meet at C
Join R , T and S , T

2 ,1 , 3

2 , 3 , 1

3 , 2 , 1

1 , 2 , 3

68. Put the following in correct order to construct 90⁰ at initial point of given ray and justify the construction

First we draw a ray $\overrightarrow{AP}$
Taking B as centre with same radius we draw a 60⁰ arc to cut the arc in step 2 at C
Taking B as centre with same radius we draw a 120⁰ arc to cut the arc in step 2 at C
Taking C and D as centres with same radius we draw 2 arcs to intersect at Q

1 , 4 , 3 , 2

1 , 3 , 4 , 2

1 , 2 , 3 , 4

4 , 3 , 2 , 1

69. Put the following in correct order to construct 45⁰ at initial point of given ray and justify the construction

First take a ray $\overrightarrow{AP}$
We draw a perpendicular bisector of $\overline{AB}$ and let 'O' be the intersecting point
Join A and C we get $\angle$ BAC = 45⁰
Mark any point B on the ray $\overrightarrow{AP}$
Taking OA as a radius and 'O' as centre we cut the perpendicular bisector with anarc andd let intersecting point be C

1 , 4 , 2 , 5 , 3

1 , 3 , 4 , 2 , 5

1 , 2 , 3 , 4 , 5

4 , 3 , 2 , 1 , 5

70. Here ab =

71. Here $\triangle$ abc is ............. triangle

Scalene

Right

Equilateral

Isosceles

72. Here $\triangle$ abo =

$\triangle$ cbo

$\triangle$ cdo

$\triangle$ aod

None

73. In the figure PQ $\perp$ XY then XP = ...............

74. In the figure $\triangle$ XPY is .................... triangle

Equilateral

Isosceles

Right angled

Scalene

75. In the figure $\triangle$ XPO

$\triangle$ YOP

$\triangle$ YOQ

$\triangle$ XOQ

$\triangle$ POX

76. Which of the following is odd one according to ruler and compass ?

37.5⁰

40⁰

22.5⁰

67.5⁰

77. Which of the following is odd one according to ruler and compass ?

37.5⁰

40⁰

47.5⁰

35⁰

78. Which of the following is odd one according to ruler and compass ?

15⁰

75⁰

22 $\frac{1}{2} ^{0}$

32 $\frac{1}{2} ^{0}$

79. Let Q be a point on perpendicular bisector of line segment CD then ,

Q is equidistant from A , B

QC : QD = 1 : 2

Q lies on CD

QC : QD = 2 : 3

80. In a right angled triangle PQR , $\angle$ P = 90⁰ , which of the following are true ?

$\angle$ P + $\angle$ R = 90⁰

PR > PQ or QR

PQ = QR

All

81. The base of semi circle is known as

Large chord

Diameter

Radius + Radius

All

82. Let XY be a line segment and PQ be the perpendicular bisector of XY which cuts at M then which of the following are true ?

XM = YM

XP = PY

$\angle$ XMP = $\angle$ PMY = 90⁰

All

83. In a triangle PQR , PQ - QR is .............. PR

None

84. Among the angles 22 $\frac{1}{2} ^{0}$ , 67 $\frac{1}{2} ^{0}$ , 82 $\frac{1}{2} ^{0}$ , 102 $\frac{1}{2} ^{0}$ only which angle can be constructed by using ruler and compass

22 $\frac{1}{2} ^{0}$

67 $\frac{1}{2} ^{0}$

82 $\frac{1}{2} ^{0}$

All

85. Among the angles 25⁰ , 35⁰ , 45⁰ , 55⁰ ............... can't be constructed by using ruler and compass

55⁰

35⁰

25⁰

All

86. In a triangle ABC , AB + BC is .... AC

None

87. Which of the following angles can be constructed by using ruler and compass only

90⁰

45⁰

Both

70⁰

88. Which of the following angles can't be constructed by using ruler and compass only

72⁰

130⁰

20⁰

All

89. In a right angle triangled , one angle is 60⁰ then other angle will be

60⁰

30⁰

20⁰

10⁰

90. Which of the following are not a right angled triangle ?

60⁰ , 60⁰

30⁰ , 30⁰

45⁰ , 45⁰

All

91. If in $\bigtriangleup$ PQR , $\overrightarrow{QX}$ , $\overrightarrow{RY}$ are bisectors to base then $\angle$ QXR =

90⁰ - $\frac{1}{2} \angle$ A

90⁰ + $\frac{1}{2} \angle$ A

180⁰ - $\frac{1}{2} \angle$ A

180⁰ + $\frac{1}{2} \angle$ A

92. If 2 base angles of triangle are given then to construct the triangle , we need

Perimeter

Base and differences of other two sides

Base and sum of other two sides

Any one of them

93. Which of the following are true ?

We can construct 45⁰ by using ruler and compass
We can construct 120⁰ by using ruler and compass

1 is true

2 is true

Both

None

94. Which of the following are true ?

We can not construct 70⁰ by using ruler and compass
We can construct 120⁰ by using ruler and compass

1 is true

2 is true

Both

None

95. In a triangle the sum of two sides is .......... hypotenuse

Greater than

Less than

Equal

Any one of them

96. In a triangle the differences of two sides is .......... hypotenuse

Greater than

Less than

Equal

Any one of them

97. In a triangle if two angles are acute then the angle is ............ 90⁰

Can't say

98. With the help of ruler and compass , it is not possible to construct an angle of

40⁰

47.5⁰

Both

37.5⁰

99. The concept of drawing geometrical figure using ungraduated ruler and a compass is

Geometry box

Geometrical construction

Both

None

100. Geometry box contains the

Set of squares

Divider

Protractor

All

AP 9th Maths Mock Test 2021 For Chapter – 13 : “Geometrical Constructions” Online Practice Test

Related Mock Tests:

Leave a Comment Cancel reply