Practice MCQ Questions and Answer on Triangles

71.

D is any point on side AC of ÃÂÃÂÃÂÃÂÃÂÃÂABC. If P, Q, X, Y are the mid-point of AB, BC, AD and DC respectively, then the ratio of PX and QY is

(A) 1 : 2
(B) 1 : 1
(C) 2 : 1
(D) 2 : 3

Solution: According to question, PX || BD [mid point theorem] ∴ PX = $\frac{1}{2}$ BD Similarly, QY || BD ∴ QY = $\frac{1}{2}$ BD ∴ PX : QY, $\frac{1}{2}$ BD : $\frac{1}{2}$ BD PX : QY = 1 : 1

72.

In ÃÂÃÂÃÂÃÂÃÂÃÂABC, ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BAC = 90ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ° and AD ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ¥ BC. If BD = 3 cm and CD = 4 cm, then length of AD is :

(A) $2 \sqrt{3}$ cm
(B) 3.5 cm
(C) 6 cm
(D) 5 cm

Solution: We know that, AD2 = CD × BD AD2 = 4 × 3 AD2 = 12 AD = $2 \sqrt{3}$ cm

73.

In ÃÂÃÂÃÂÃÂÃÂÃÂABC, ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ A + ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B = 65ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B + ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ C = 140ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then find ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B.

(A) 40°
(B) 25°
(C) 35°
(D) 20°

74.

ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ ABC = 30ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BCD is equal to

(A) 45°
(B) 90°
(C) 30°
(D) 60°

Solution: According to question, In ΔABC Exterior angle CAD = ∠ABC + ∠ACB CAD = 2∠ABC (∵ ∠ABC = ∠ACB) CAD = 2 × 30° CAD = 60° In ΔCAD, ∠ACD = ∠ADC = $\frac{180 - ∠ CAD}{2}$ = 60° ⇒ ∠BCD = ∠ACD + ∠BCA ⇒ ∠BCD = 60° + 30° ⇒ ∠BCD = 90°

75.

In a ÃÂÃÂÃÂÃÂÃÂÃÂABC, If 2ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ A = 3ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B = 6ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ C, then the value of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B is:

(A) 60°
(B) 30°
(C) 45°
(D) 90°

Solution: According to question, Given : $\begin{aligned} 2 ∠ A = 3 ∠ B \\ \frac{∠ A}{∠ B} = \frac{3}{2} 3 ∠ B = 6 ∠ C \\ \frac{∠ B}{∠ C} = \frac{6}{3} = \frac{2}{1} \end{aligned}$ To make angle ∠B same ∴ ∠A : ∠B : ∠C 3 : 2 : 1 As we know that ∠A + ∠B + ∠C = 180° 3x + 2x + x = 180° x = 30° ∠B = 2x ∠B = 60°

76.

The circumcentre of a triangle ABC is O. If ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BAC = 85ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ° and ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BCA = 75ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then the value of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ OAC is

(A) 40°
(B) 60°
(C) 70°
(D) 90°

77.

In a triangle ABC, BC is produced to D so that CD = AC. If ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BAD = 111ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ° and ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ ACB = 80ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then the measure of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ ABC is:

(A) 31°
(B) 33°
(C) 35°
(D) 29°

78.

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

79.

The orthocenter of a triangle is the point where?

(A) The medians meet
(B) The altitudes meet
(C) The right bisectors of the sides of
(D) The bisectors of the angles

80.

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) $\frac{11}{2}$

Solution: According to question, AB + BC = 12 cm BC + CA = 14 cm CA + AB = 18 cm 2(AB + BC + CA) = 44 cm AB + BC + CA = $\frac{44}{2}$ cm AB + BC + CA = 22 cm Perimeter of triangle = 22 cm Perimeter of triangle = Perimeter of circle 22 = 2πr 2 × $\frac{22}{7}$ × r = 22 r = $\frac{7}{2}$ cm

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Practice MCQ Questions and Answer on Triangles

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