26. The centroid of the triangle with vertices (-1, 4), (5, -2) and (2, 7) is:
- (3, 2)
- (6, 9)
- (2, 3)
- (2, 1)
Answer: C) (2, 3)
Explanation: Centroid = ( x1 + x2 + x33, y1 + y2 + y33 ) = (2, 3). SLO M-09-B-31 · Understanding
MCQs / Mathematics / Construction of Triangles
Construction of Triangles MCQs — Mathematics (page 2)
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.
27. The three medians of a triangle meet at the:
- centroid
- circumcentre
- orthocentre
- incentre
Answer: A) centroid
Explanation: A median joins a vertex to the midpoint of the opposite side. SLO M-09-B-31 · Understanding
28. In an SSA construction, the arc for the third vertex is drawn with radius equal to:
- the height of the triangle
- the side adjacent to the given angle
- the side opposite the given angle
- the sum of the two sides
Answer: C) the side opposite the given angle
Explanation: Centre at the end of the adjacent side; radius is the opposite side. SLO M-09-B-30 · Knowledge
29. In an ASA construction, after drawing the given side AB, the next step is to:
- draw a circle on AB
- draw the perpendicular bisector of AB
- draw the given angles at A and B on the same side of AB
- mark a third point with a compass
Answer: C) draw the given angles at A and B on the same side of AB
Explanation: The arms of the two angles meet at the third vertex C. SLO M-09-B-29 · Knowledge
30. A triangle with base 5 cm and base angles of 60^circ each is:
- equilateral with all sides 5 cm
- isosceles with sides 5, 5, 6 cm
- scalene
- right-angled
Answer: A) equilateral with all sides 5 cm
Explanation: All angles are 60^circ, so all sides are equal. SLO M-09-B-29 · Knowledge
31. For ASA data, which condition must the two angles satisfy?
- their sum must be 180^circ
- one must be 90^circ
- they must be equal
- their sum must be less than 180^circ
Answer: D) their sum must be less than 180^circ
Explanation: The third angle must be positive. SLO M-09-B-29 · Knowledge
32. The centroid of the triangle with vertices (0, 0), (6, 0) and (3, 9) is:
- (3, 0)
- (3, 3)
- (4, 3)
- (9, 9)
Answer: B) (3, 3)
Explanation: Centroid = ( x1 + x2 + x33, y1 + y2 + y33 ) = (3, 3). SLO M-09-B-31 · Understanding
33. How many triangles ABC can be constructed with angle A = 90^circ, b = AC = 5 cm and a = BC = 7 cm?
- 0
- 2
- 1
- 3
Answer: C) 1
Explanation: With angle A = 90^circ (not acute), the side opposite A must be the longest. Here a = 7 b = 5, so there is one triangle. SLO M-09-B-30 · Knowledge
34. The RHS (right angle–hypotenuse–side) case is a special case of:
- ASA
- SSA
- SSS
- SAS
Answer: B) SSA
Explanation: Two sides and an angle not between them — but with the angle a right angle there is no ambiguity. SLO M-09-B-30 · Knowledge
35. To construct the perpendicular bisector of AB, you draw arcs from A and B with radius:
- more than half of AB
- exactly AB only
- any length at all
- less than half of AB
Answer: A) more than half of AB
Explanation: The arcs must cross above and below AB. SLO M-09-B-31 · Understanding
36. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 6 cm and a = BC = 9 cm?
- 1
- 3
- 0
- 2
Answer: A) 1
Explanation: The height from C is h = bsin A = 6 12 = 3 cm. Since a = 9 ge b = 6, the arc cuts the base line on only one side of A: one triangle. SLO M-09-B-30 · Knowledge
37. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 12 cm and a = BC = 10 cm?
- 1
- 2
- 0
- 3
Answer: B) 2
Explanation: The height from C is h = bsin A = 12 12 = 6 cm. Since h < a < b (6 < 10 < 12), the arc cuts the base twice: two triangles (the ambiguous case). SLO M-09-B-30 · Knowledge
38. When SSA data gives two triangles, the two angles at B (call them B1 and B2) are:
- equal
- complementary
- supplementary (B1 + B2 = 180^circ)
- both right angles
Answer: C) supplementary (B1 + B2 = 180^circ)
Explanation: The two positions of B form an isosceles triangle with C, so the angles add to 180^circ. SLO M-09-B-30 · Knowledge
39. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 8 cm and a = BC = 6 cm?
- 0
- 2
- 1
- 3
Answer: B) 2
Explanation: The height from C is h = bsin A = 8 12 = 4 cm. Since h < a < b (4 < 6 < 8), the arc cuts the base twice: two triangles (the ambiguous case). SLO M-09-B-30 · Knowledge
40. How many triangles ABC can be constructed with angle A = 30^circ, b = AC = 10 cm and a = BC = 12 cm?
- 2
- 1
- 3
- 0
Answer: B) 1
Explanation: The height from C is h = bsin A = 10 12 = 5 cm. Since a = 12 ge b = 10, the arc cuts the base line on only one side of A: one triangle. SLO M-09-B-30 · Knowledge
41. Given one side and two angles (ASA), how many different triangles can be constructed?
- two
- infinitely many
- exactly one
- none
Answer: C) exactly one
Explanation: ASA fixes the triangle (ASA congruence). SLO M-09-B-29 · Knowledge
42. If the two given angles in an ASA construction are drawn on opposite sides of the base:
- an isosceles triangle is formed
- their arms will not meet to form a triangle
- two triangles are formed
- a larger triangle is formed
Answer: B) their arms will not meet to form a triangle
Explanation: Both angles must be drawn on the same side of the base. SLO M-09-B-29 · Knowledge
43. In the ambiguous case with acute angle A, two triangles are possible when:
- a b
- a = bsin A
- bsin A < a < b
- a < bsin A
Answer: C) bsin A < a < b
Explanation: The arc of radius a about C crosses the base line at two points on the same side of A. SLO M-09-B-30 · Knowledge
44. Can a triangle be constructed with two angles 45^circ and 90^circ?
- Yes
- No
- Only if the side is longer than 10 cm
- Only if one angle is 90^circ
Answer: A) Yes
Explanation: The two angles add to 135^circ, which is less than 180^circ, so a triangle can be made. SLO M-09-B-29 · Knowledge
45. To construct triangle PQR given moverlinePQ, moverlineQR and the included angle, the angle needed is:
- angle P
- any angle of the triangle
- angle Q
- angle R
Answer: C) angle Q
Explanation: The included angle lies between the two given sides; PQ and QR meet at Q. SLO M-09-B-28 · Knowledge
46. In a right-angled triangle, the circumcentre lies:
- at the midpoint of the hypotenuse
- at the centroid
- at the right-angled vertex
- outside the triangle
Answer: A) at the midpoint of the hypotenuse
Explanation: The hypotenuse is a diameter of the circumcircle. SLO M-09-B-31 · Understanding
47. How many triangles ABC can be constructed with angle A = 120^circ, b = AC = 5 cm and a = BC = 8 cm?
- 1
- 2
- 0
- 3
Answer: A) 1
Explanation: With angle A = 120^circ (not acute), the side opposite A must be the longest. Here a = 8 b = 5, so there is one triangle. SLO M-09-B-30 · Knowledge
48. To construct triangle ABC given moverlineAB, moverlineBC and the included angle, the angle needed is:
- angle A
- angle C
- any angle of the triangle
- angle B
Answer: D) angle B
Explanation: The included angle lies between the two given sides; AB and BC meet at B. SLO M-09-B-28 · Knowledge
49. The median from A in triangle A(0, 6), B(-2, 0), C(4, 0) meets BC at:
- (2, 0)
- (1, 3)
- (0, 0)
- (1, 0)
Answer: D) (1, 0)
Explanation: The median goes to the midpoint of BC: ( -2 + 42, 0 ) = (1, 0). SLO M-09-B-31 · Understanding
50. In a right-angled triangle, the orthocentre lies:
- at the incentre
- outside the triangle
- at the vertex of the right angle
- at the midpoint of the hypotenuse
Answer: C) at the vertex of the right angle
Explanation: Two of the altitudes are the legs themselves, and they meet at the right angle. SLO M-09-B-31 · Understanding
Practise Construction of Triangles MCQs