MCQs / Mathematics / Construction of Triangles

Construction of Triangles MCQs — Mathematics (page 4)

87 multiple-choice questions on Construction of Triangles from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

76. An angle of 60^circ in a construction can be made with:

  1. it cannot be constructed
  2. a compass and ruler only
  3. a set-square only
  4. a protractor only

Answer: B) a compass and ruler only

Explanation: Equal arcs from the vertex form an equilateral triangle, giving 60^circ. SLO M-09-B-28 · Knowledge

Discuss this question

77. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 10 cm and a = BC = 4 cm?

  1. 2
  2. 0
  3. 1
  4. 3

Answer: B) 0

Explanation: The height from C is h = bsin A = 10 12 = 5 cm. Since a = 4 < h, the arc cannot reach the base: no triangle. SLO M-09-B-30 · Knowledge

Discuss this question

78. A triangle is to be constructed with angle A = 110^circ and angle B = 30^circ. The third angle will be:

  1. 220^circ
  2. 40^circ
  3. 50^circ
  4. 140^circ

Answer: B) 40^circ

Explanation: angle C = 180^circ - 110^circ - 30^circ = 40^circ. SLO M-09-B-29 · Knowledge

Discuss this question

79. The centroid divides each median in the ratio (from the vertex):

  1. 3 : 1
  2. 1 : 1
  3. 2 : 1
  4. 1 : 2

Answer: C) 2 : 1

Explanation: The centroid is two-thirds of the way from each vertex along the median. SLO M-09-B-31 · Understanding

Discuss this question

80. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 10 cm and a = BC = 7 cm?

  1. 3
  2. 1
  3. 2
  4. 0

Answer: C) 2

Explanation: The height from C is h = bsin A = 10 12 = 5 cm. Since h < a < b (5 < 7 < 10), the arc cuts the base twice: two triangles (the ambiguous case). SLO M-09-B-30 · Knowledge

Discuss this question

81. A triangle is to be constructed with angle A = 35^circ and angle B = 85^circ. The third angle will be:

  1. 240^circ
  2. 70^circ
  3. 120^circ
  4. 60^circ

Answer: D) 60^circ

Explanation: angle C = 180^circ - 35^circ - 85^circ = 60^circ. SLO M-09-B-29 · Knowledge

Discuss this question

82. A triangle is constructed with two sides 9 cm and 12 cm and an included angle of 90^circ. When measured, the third side should be:

  1. 21 cm
  2. 3 cm
  3. 15 cm
  4. 16 cm

Answer: C) 15 cm

Explanation: By Pythagoras the third side is 9^2 + 12^2 = 15 cm — a useful check on the accuracy of the construction. SLO M-09-B-28 · Knowledge

Discuss this question

83. How many triangles ABC can be constructed with angle A = 120^circ, b = AC = 8 cm and a = BC = 5 cm?

  1. 1
  2. 3
  3. 2
  4. 0

Answer: D) 0

Explanation: With angle A = 120^circ (not acute), the side opposite A must be the longest. Here a = 5 < b = 8, so there is no triangle. SLO M-09-B-30 · Knowledge

Discuss this question

84. A right triangle has legs 5 cm and 12 cm. The radius of its circumcircle is:

  1. 172 cm
  2. 5 cm
  3. 132 cm
  4. 13 cm

Answer: C) 132 cm

Explanation: The hypotenuse = 13 cm is a diameter, so R = 132 cm. SLO M-09-B-31 · Understanding

Discuss this question

85. A triangle is constructed with two sides 6 cm and 8 cm and an included angle of 90^circ. When measured, the third side should be:

  1. 14 cm
  2. 2 cm
  3. 11 cm
  4. 10 cm

Answer: D) 10 cm

Explanation: By Pythagoras the third side is 6^2 + 8^2 = 10 cm — a useful check on the accuracy of the construction. SLO M-09-B-28 · Knowledge

Discuss this question

86. In ASA data for triangle ABC the angles given are angle A and angle B. The side given must be:

  1. any side
  2. overlineBC
  3. overlineAC
  4. overlineAB

Answer: D) overlineAB

Explanation: In ASA the side lies between the two given angles, i.e. joins A and B. SLO M-09-B-29 · Knowledge

Discuss this question

87. A triangle is to be constructed with angle A = 64^circ and angle B = 64^circ. The third angle will be:

  1. 128^circ
  2. 232^circ
  3. 62^circ
  4. 52^circ

Answer: D) 52^circ

Explanation: angle C = 180^circ - 64^circ - 64^circ = 52^circ. SLO M-09-B-29 · Knowledge

Discuss this question

Previous Page 4 of 4

Practise Construction of Triangles MCQs

More Mathematics chapters