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

1. The construction of a \bigtriangleupABC in which AB = 8 cm , \angleA = 450 is possible when (BC + AC) is
2. The construction of a \trianglePQR in  which PQ = 7 cm \angleP = 750 is possible when (QR - PR) is.............
3. The construction of a \triangleABC in  which BC = 6.4 cm \angleB = 600 is not possible when (AB + AC) is.............
4. The process of drawing geometrical figure by using a compass and ungraduated ruler is called ...........
5. In a right angle triangle , one angle is 300 then the other angle is
6. The construction of triangle ABC in which BC = 6 cm , \angleB = 450 is not possible when difference of AB and AC is equal
7. The construction of triangle ABC in which AB = 4 cm , \angleA = 600 is not possible when difference of BC and AC is equal to
8. The construction of triangle ABC , given that BC = 3 cm , \angleC = 600 is possible when difference of AB and AC is equal to
9. The construction of \triangle DEF , given that DE = 7 cm , \angleD = 750 is possible when (EF - DF) is equal to
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 \anglePOM = ..............
11. The construction of \triangleABC in which AB = 5 cm , \angleA = 750 is possible when (BC - AC) is equal to
12. Which of the following angles can be constructed by using ruler and compass only
13. Which of the following angles can not be constructed by using ruler and compass only
14. In a triangle PQR , PQ + QR is .............PR
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
16. Among the angles 250 , 350 , 450 , 550 only ...................... can be constructed by using ruler and compass
17. In a triangle ABC , AB - BC is ..................
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 ?
19. The angle in the semicircle is ..............
20. In a right angled triangle ABC with \angleB = 900 , which of the following are true ?
  1. \angleA + \angleC = 900
  2. AC > Ab or BC
  3. AB = BC
21. In a triangle if two angles are acute then the angle is
22. Let P be a point on a perpendicular bisector of a line segment \overline{AB}then
23. Which of the following angles cannot be constructed using ruler and compass only ?
24. With the help of of a ruler and a compass , it is possible to construct an angle of ...............
25. With the help of of a ruler and a compass , it is not possible to construct an angle of ...............
26. Which of the following statements are true ?
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
28. If perimeter of a triangle is given then to construct the triangle , we need
29. If base and one of the base angle is given , then what is the third condition required to construct a triangle
  1. Sum of other two sides
  2. Sum of other two angles
  3. Differences of other two angles
  4. Difference of other two sides
30. Which of the following conditions are sufficient to construct a triangle ?
31. Observe the  steps of the following
  1. With P as centre and radius (>\frac{1}{2}PQ) draw an arc
  2. Given an angle BAC
  3. With A as centre with many radius , draw an arc , cutting \overline{AB}\overline{AC} at P and Q respectively
  4. Join AR and produce to obtain ray \overrightarrow{AX}
  5. 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 \angleBAC
32. A perpendicular bisector of a given line segment LM can be constructed using following steps given without order , put them in an order
  1. Join RS intersecting LM at P , then P bisects the line segment LM
  2. Let these arcs intersect each other at R and S
  3. 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
  4. Join LR , RM MS and LS
33. Put the following steps in order to construct an angle 600 at 'O' of a given ray  \overrightarrow{OA}
  1. With centre O and any radius , draw an arc PQ cutting the ray OA at P
  2. Join OR an d produce it to obtain a ray  \overrightarrow{OB}
  3. Draw a ray  \overrightarrow{OA}
  4. With centre P and the same radius as above , draw an arc cutting the arc PQ at R
  5.  \angleAOB so obtained is the angle of measure 600
 
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
36. In the figure , if XY is perpendicular bisector of PQ then triangle PXO =
37. Arrange the following steps of construction of a triangle ABC in which BC = 8 cm , \angleB = 300 and Ab + Ac = 2 cm in order
  1. PQ intersects BD at A and CD at L
  2. Join CD
  3. Draw BC = 8 cm
  4. Construct \angleCBX = 300
  5. Draw PQ , the perpendicular  bisector of CD
  6. Join CA
  7. Along BX , cut BD = 12 cm
38. We have to construct a \triangle ABC such that BC = 6 cm , \angleB = 450 and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and \angleCBX = 450
From the data , in the next step of construction we produce XB to D so that
39. We have to construct a \triangle ABC such that BC = 6 cm , \angleB = 450 and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and \angleCBX = 450
From the data , next we join CD and draw PQ which is ............. of CD
40. We have to construct a \triangle ABC such that BC = 6 cm , \angleB = 450 and AC - AB = 2 cm . For this , we start the construction by drawing BC = 6 cm and \angleCBX = 450
From the data , Let PQ intersects BX at A and CD at L then what is next step ?
41. In the figure XY perpendicular to AB then Ax =
42. In the figure triangle AXB is
43. In the figure \triangleAXO \cong =
44. In the figure \overrightarrow{BD} is the bisector of \angleABC then
45. If in \triangleABC , \overrightarrow{BX} and \overrightarrow{CY} are bisectors to the base then \angleBXC =
46. Arrange the following steps in order if we construct a bisector of a line segment
  1. Draw a line segment
  2. Join EF intersecting AB at M , then M bisects the line segment AB as shown in figure
  3. With centre A and radius more than half of AB , draw arcs , one on each sides of AB
  4. With B as centre and the same radius as before , draw arcs , cutting the previously drawn arcs at E and F respectively
47. To construct an angle bisector , arrange the following steps in order
  1. Join AR and produce it to any point X . the ray AX is the required bisector of \angleBAC
  2. With centre Q and the same radius draw another arc intersecting previous arc
  3. With centre 'P' and radius more than \frac{1}{2}PQ draw an arc
  4. With centre A and any convenient radius draw an arc cutting AB and AC at P and Q respectively
48. To construct a circle segment given a
49. To construct a triangle , we need
50. To construct a triangle we need
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
53. The box containing a graduated ruler , a pair of set squares , a divider , a compass and a protractor is called
54. Each angle of an equilateral triangle is
55. The angle in a semicircle is
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
  1. Draw a line segment \overline{AB} = 5 cm
  2. Mark any point 'C' on the semi - circle and join AC and AB to form \angleACB = 900
  3. Taking OA or OB as radius with centre 'O' draw a semi circle
  4. Draw the perpendicular bisector of AB to cut at 'O'
58. Construct a segment of a circle on a chord of length 5 cm . containing the angle 450
  1. Draw two rays \overrightarrow{AX}\overrightarrow{BY} at A , B such that they meet at 'O'
  2. Mark the point 'C' such that
  3. Taking OA or OB as radius with centre 'O' draw a circle
  4. Draw a line segment AB = 5 cm
59. Construct a segment of a circle on a chord of length 5 cm . containing the angle 1200
  1. Mark the point 'C' on AZB sector . \angle ACB = 1200
  2. Taking 'O' as centre and with OA or OB as radius draw a circle
  3. Draw \overrightarrow{AX}\overrightarrow{BY} rays such that they meet at 'O' . So \angle BAX = \angleABY = 300
  4. Draw a line segment AB = 5 cm
 
60. Construct a right angled triangle whose base is 7.5 cm and sum of its hypotenuse and other side is 15 cm
  1. Draw the base BC = 7.5 cm and construct \angleCBX = 900 at B
  2. Taking B as centre and radius as 15 cm ( = AB + AC ) , draw an arc to meet \overrightarrow{BX} at D
  3. Join \overline{CD} and draw the perpendicular bisector of CD ,let it be met \overrightarrow{BD} at A
  4. Join \overline{AC} to form \triangleABC
61. Construct XYZ in which \angleY = 300 , \angleZ = 600 and XY + YZ + ZX = 10 cm
  1. Draw line segment AB = 10 cm
  2. Join XY and XZ
  3. Construct \angleBAL= 300 and \angleABM = 600
  4. Draw perpendicuular bisectors of AX and BX and let them meet the line segment AB at Y and Z respectively
  5. Draw angular bisectors of \angleA and \angleB to meet at X
62. Construct \trianglePQR in which QR = 8 cm , \triangleQ = 600 and PQ - PR = 3.5 cm
  1. Join PR to get the required triangle PQR
  2. Draw the perpendicular bisectors of SR and let it meet the ray \overline{QX} at the point 'P'
  3. First construct the triangle QRS using SAS rule with measures QR = 8 cm , QS = 3.5 cm and \angleQ = 600
63. Construct \triangleABC in which BC = 7 cm , \angleB = 750 and AB + AC = 12 cm
  1. Join \overline{AC} to get the required triangle
  2. Join CD and draw perpendicular bisector of \overline{CD} to meet \overline{BD} at A
  3. Draw the base BC = 7 cm and construct \angleCBX = 750 at B
  4. With centre B and radius 12 cm(+AB + AC) draw an arc on \overline{BX} to meet at D
64. Construct an iscosceles triangle , given its base AB as 5 cm and \angleA = 500
  1. Let the point of intersection of two rays be 'C'
  2. Draw a ray making same angle 500 at B
  3. Draw a ray making same angle 500 at A
  4. Draw a line segment AB of length 5 cm
65. Construct an iscosceles triangle , given its base PQ as 10 cm and \angleP = 600
  1. Let the point of intersection of two rays be 'R'
  2. Draw a ray making same angle 600 at Q
  3. Draw a ray making same angle 600 at P
  4. Draw a line segment PQ of length 10 cm
66. Write the correct order for construct an equilateral triangle , given its side length 4.5 cm and justify the construction
  1. Draw a line segment AB of any length say 4.5 cm
  2. 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
  3. Join A , C and B , C
67. Write the correct order for construct an equilateral triangle , given its side length 5.5 cm and justify the construction
  1. Draw a line segment RS of any length say 4.5 cm
  2. 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
  3. Join R , T and S , T
68. Put the following in correct order to construct 900 at initial point of given ray and justify the construction
  1. First we draw a ray \overrightarrow{AP}
  2. Taking B as centre with same radius we draw a 600 arc to cut the arc in step 2 at C
  3. Taking B as centre with same radius we draw a 1200 arc to cut the arc in step 2 at C
  4. Taking C and D as centres with same radius we draw 2 arcs to intersect at Q
69. Put the following in correct order to construct 450 at initial point of given ray and justify the construction
  1. First  take a ray \overrightarrow{AP}
  2. We draw a perpendicular bisector of \overline{AB} and let 'O' be the intersecting point
  3. Join A and C we get \angleBAC = 450
  4. Mark any point B on the ray \overrightarrow{AP}
  5. Taking OA as a radius and 'O' as centre we cut the perpendicular bisector with anarc andd let intersecting point be C
70. Here     ab =
71. Here \triangleabc is ............. triangle
72. Here \triangleabo =
73. In the figure PQ \perpXY then XP = ...............
74. In the figure  \triangleXPY  is .................... triangle
75. In the figure \triangleXPO
76. Which of the following is odd one according to ruler and compass ?
77. Which of the following is odd one according to ruler and compass ?
78. Which of the following is odd one according to ruler and compass ?
79. Let Q be a point on perpendicular bisector of line segment CD then ,
80. In a right angled triangle PQR , \angleP = 900 , which of the following are true ?
81. The base of semi circle is known as
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 ?
83. In a triangle PQR , PQ - QR is .............. PR
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
85. Among the angles 250 , 350 , 450 , 550 ............... can't be constructed by using ruler and compass
86. In a triangle ABC , AB + BC is .... AC
87. Which of the following angles can be constructed by using ruler and compass only
88. Which of the following angles can't be constructed by using ruler and compass only
89. In a right angle triangled , one angle is 600 then other angle will be
90. Which of the following are not a right angled triangle ?
91. If in \bigtriangleupPQR , \overrightarrow{QX} , \overrightarrow{RY} are bisectors to base then \angleQXR =
92. If 2 base angles of triangle are given then to construct the triangle , we need
93. Which of the following are true ?
  1. We  can construct 450 by using ruler and compass
  2. We can construct 1200 by using ruler and compass
94. Which of the following are true ?
  1. We  can not construct 700 by using ruler and compass
  2. We can construct 1200 by using ruler and compass
95. In a triangle the sum of two sides is .......... hypotenuse
96. In a triangle the differences of two sides is .......... hypotenuse
97. In a triangle if two angles are acute then the angle is ............ 900
98. With the help of ruler and compass , it is not possible to construct an angle of
99. The concept of drawing geometrical figure using ungraduated ruler and a compass is
100. Geometry box contains the

 

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