Practice MCQ Questions and Answer on Triangles

1.

A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

  • (A) AB2 + CD2 = AD2 + BC2
  • (B) CD2 + BD2 = 2AD2
  • (C) AB2 + AC2 = 2AD2
  • (D) AB2 = AD2 + BC2

2.

If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, âˆÂ BGC = 60°, BC = 8 cm, then area of the triangle ABC is:

  • (A) $$96\sqrt 3 $$  cm2
  • (B) $$48\sqrt 3 $$  cm2
  • (C) 48 cm2
  • (D) $$54\sqrt 3 $$  cm2

3.

Length of the sides of a triangle are a, b and c respectively. If a2 + b2 + c2 = ab + bc + ca then the triangle is:

  • (A) Isosceles
  • (B) Equilateral
  • (C) Scalene
  • (D) Right-angled

4.

An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and âˆÂ BAD = 15°, sin 75° = ?

  • (A) $$\frac{{2b}}{{\sqrt 3 a}}$$
  • (B) $$\frac{a}{{2b}}$$
  • (C) $$\frac{{\sqrt 3 a}}{{2b}}$$
  • (D) $$\frac{{2a}}{{\sqrt 3 b}}$$

5.

In ΔABC, âˆÂ A + âˆÂ B = 65°, âˆÂ B + âˆÂ C = 140°, then find âˆÂ B.

  • (A) 40°
  • (B) 25°
  • (C) 35°
  • (D) 20°

6.

In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle

  • (A) $$\frac{5}{2}$$
  • (B) $$\frac{7}{2}$$
  • (C) $$\frac{9}{2}$$
  • (D) $$\frac{{11}}{2}$$

7.

Which of the following is a true statement

  • (A) Two similar triangles are always congruent
  • (B) Two similar triangles have equal areas
  • (C) Two triangles are similar if their corresponding sides are proportional
  • (D) Two polygons are similar if their corresponding sides are proportional

8.

I is the incentre of a triangle ABC. If âˆÂ ACB = 55°, âˆÂ ABC = 65° then the value of âˆÂ BIC is

  • (A) 130°
  • (B) 120°
  • (C) 140°
  • (D) 110°

9.

In ΔABC âˆÂ A = 90° and AD âŠÂ¥ BC where D lies on BC. If BC = 8 cm, AD = 6 cm, then arΔABC : arΔACD = ?

  • (A) 4 : 3
  • (B) 25 : 16
  • (C) 16 : 9
  • (D) 25 : 9

10.

Incenter of ΔABC is I. âˆÂ ABC = 90° and âˆÂ ACB = 70°. âˆÂ BIC is:

  • (A) 115°
  • (B) 100°
  • (C) 110°
  • (D) 105°

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