Practice MCQ Questions and Answer on Triangles

91.

In ÃÂÃÂÃÂÃÂÃÂÃÂABC, two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. Then ÃÂÃÂÃÂÃÂÃÂÃÂABC and ÃÂÃÂÃÂÃÂÃÂÃÂDBE are :

(A) Similar only if D lies outside the line segment AB
(B) Congruent only If D lies out side the line segment AB
(C) Always similar
(D) Always congruent

92.

In ÃÂÃÂÃÂÃÂÃÂÃÂABC, ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B = 60ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ° and ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ C = 40ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°. If AD and AE be respectively the internal bisector of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ A and perpendicular on BC, then the measure of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ DAE is

(A) 5°
(B) 10°
(C) 40°
(D) 60°

Solution: According to question, Given : ∠B = 60° ∠C = 40° As we know that ∠A + ∠B + ∠C = 180° ∠A = 180° - 60° - 40° ∠A = 80° ∴ ∠BAD = $\frac{80^{\circ}}{2}$ = 40° In ΔAEB ∠A + ∠B + ∠E = 180° ∠A = 180° - 60° - 90° ∠A = 30° Then, ∠DAE = ∠DAB - ∠EAB ∠DAE = 40° - 30° ∠DAE = 10° By Trick $\begin{aligned} ∠ D A E = \frac{∠ B - ∠ C}{2} \\ = \frac{60^{\circ} - 40^{\circ}}{2} \\ = 10^{\circ} \end{aligned}$

93.

Possible length of the sides of a triangle are:

(A) 2cm, 3cm, 6cm
(B) 3cm, 4cm, 5cm
(C) 2.5cm, 3.5cm, 6cm
(D) 4cm, 4cm, 9cm

94.

In a ÃÂÃÂÃÂÃÂÃÂÃÂABC, AB = AC and BA is produced to D such that AC = AD. Then the ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BCD is :

(A) 100°
(B) 60°
(C) 80°
(D) 90°

95.

In a triangle ABC, incentre is O and ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BOC = 110ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then the measure of ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ BAC is:

(A) 20°
(B) 40°
(C) 55°
(D) 110°

Solution: According to question, Given : ∠BOC = 110° ∠BOC = 90° + $\frac{1}{2}$ ∠A 110° = 90° + $\frac{∠ A}{2}$ $\frac{∠ A}{2}$ = 20 ∠A = 40°

96.

In ÃÂÃÂÃÂÃÂÃÂÃÂABC and ÃÂÃÂÃÂÃÂÃÂÃÂDEF, AB = DE and BC = EF, then one can infer that ÃÂÃÂÃÂÃÂÃÂÃÂABC ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂ ÃÂÃÂÃÂÃÂÃÂÃÂDEF, when

(A) ∠BAC = ∠EFD
(B) ∠ACB = ∠EDF
(C) ∠ABC = 2∠DEF
(D) ∠ABC = ∠DEF

97.

Let ÃÂÃÂÃÂÃÂÃÂÃÂABC and ÃÂÃÂÃÂÃÂÃÂÃÂABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be

(A) ΔABD = $\frac{1}{3}$ ΔABC
(B) ΔABD = $\frac{1}{2}$ ΔABC
(C) ΔABC = $\frac{1}{2}$ ΔABD
(D) ΔABC = ΔABD

98.

In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is

(A) 120°
(B) 60°
(C) 30°
(D) 90°

Solution: According to question, Given : AB = AC y = 2(x + x) y = 4x ∴ x + x + y = 180° 2x + 4x = 180° 6x = 180° x = $\frac{180^{\circ}}{6}$ x = 30°

99.

If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is -

(A) 8 cm
(B) 6 cm
(C) 5 cm
(D) 4.8 cm

Solution: According to question, Length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, this is right angle triangle. Note: In right angle triangle median divides the hypotenuse in two equal parts ∴ BD = $\frac{H}{2}$ BD = $\frac{10}{2}$ BD = 5 cm

100.

ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ A + $\frac{1}{2}$ ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B + ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ C = 140ÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ°, then ÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂÃÂÃÂ B is :

(A) 50°
(B) 80°
(C) 40°
(D) 60°

Solution: According to question, ∠A + $\frac{1}{2}$ ∠B + ∠C = 140° . . . . . . . . (i) As we know that ∠A + ∠B + ∠C = 180° . . . . . . . . . (ii) Compare equation (i) and (ii) $\frac{1}{2}$ ∠B = 40° ∴ ∠B = 80°

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Practice MCQ Questions and Answer on Triangles

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