CBSE Class 9 Maths Triangles MCQs

Question. Line segment joining the mid point of any side with the opposite vertex is
(a) altitude
(b) median
(c) perpendicular bisector
(d) angle bisector

Question. The length of perpendicular drawn from the opposite vertex to any side is
(a) altitude
(b) median
(c) perpendicular bisector
(d) angle bisector

Question. The point of intersection of all the altitudes of a triangle is
(a) orthocentre
(b) incentre
(c) circumcentre
(d) centroid

Question. The point of intersection of the perpendicular bisector of all sides of a triangle is
(a) orthocentre
(b) incentre
(c) circumcentre
(d) centroid

Question. In a triangle, the angle opposite to the longest side is:
(a) greater than 60°
(b) measure of 50° 
(c) greater than 90° 
(d) none of these

Question. The point of intersection of all the medians of a triangle is
(a) orthocentre
(b) incentre
(c) circumcentre
(d) centroid

Question. In a triangle ABC, if 2∠B = 6∠C, then the measure of ∠A is
(a) 30°
 (b) 75° 
(c) 90° 
(d) 60°

Question. In a triangle ABC, if 2∠A = 3∠B = 6∠C, then the measure of∠B is
(a) 30° 
(b) 75° 
(c) 90° 
(d) 60°

Question. In a triangle ABC, if 2∠A = 3∠B = 6∠C, then the measure of ∠C is
(a) 30° 
(b) 75° 
(c) 90° 
(d) 60°

Question. In a triangle ABC, if ∠A –∠B = 33° and ∠B – ∠C = 18°, then the measure of∠A is
(a) 88° 
(b) 55° 
((c) 37° 
(d) 60°

Question. In a triangle ABC, if ∠A – ∠B = 33° and ∠B – ∠C = 18°, then the measure of ∠B is
(a) 88° 
(b) 55° 
(c) 37° 
(d) 60°

Question. In a triangle ABC, if ∠A – ∠B = 33° and ∠B –∠C = 18°, then the measure of ∠C is
(a) 88° 
(b) 55° 
(c) 37° 
(d) 60°

Question. In a triangle ABC, if ∠A + ∠B = 65° and ∠B ∠C = 140°, then the measure of ∠A is
(a) 40° 
(b) 25° 
(c) 115° 
(d) 60°

Question. In a triangle ABC, if ∠A +∠B = 65° and ∠B + ∠C = 140°, then the measure of ∠B is
(a) 40° 
(b) 25° 
(c) 115° 
(d) 60°

Question. In a triangle ABC, if ∠A + ∠B = 65° and ∠B + ∠C = 140°, then the measure of ∠C is
(a) 40° 
(b) 25° 
(c) 115° 
(d) 60°

Question. In quadrilateral ABCD, AC = AD and AB bisect

(a) BC > BD
(b) BC < BD
(c) BC = BD
(d) BC = (1/2)BD

Question. In quadrilateral ABCD, AD = BC and

(a) ∠ABD > ∠BAC
(b) ∠ABD < ∠BAC
(c) ∠ABD = ∠BAC
(d) ∠ABD = (1/2)∠BAC

Question. ∠ABC is right triangle in which ∠A = 90⁰ and AB = AC.
The values of ∠B and ∠D will be
(a) ∠B = ∠C = 60⁰
(b) ∠B = ∠C = 30⁰
(c) ∠B = ∠C = 45⁰
(d) ∠B = ∠C = 50⁰

Question. The measure of each angle of an equilateral triangle is:
(a) 60°
(b) 30°
(c) 45° 
(d) 40°

Question. If the vertical angle of a isosceles triangle is 400 then measure of other two angles will be
(a) 60°, 60°
(b) 70° , 70°
(c) 50°, 50° 
(d) 75°, 75°

Question. If <A, <B and <C of ΔABC are equal then triangle is:

(a) Equilateral
(b) Isosceles
(c) Scalene
(d) none of these.

Question. AC and BD are equal perpendicular to line segment AB. If ΔBOC = ΔAOD, then the relation between OC and OD is
(a) OD > OC
(b) OD < OC
(c) OD = OC
(d) OD = (1/2)OC

Question. If M is the midpoint of hypotenuse Ac of right triangle ABC then BM = 1/2____
(a) AC
(b) BC
(c) AB
(d) none of these

Question. In fig. AB = AC and BF = CD. If ΔACD≈ΔABE then AD =

(a) AC
(b) AE
(c) AB
(d) none of these

Question. In a triangle, the angle opposite to the longer side is:
(a) larger
(b) 90°
(c) smaller
(d) none of these

Question. In a triangle side opposite to larger angle is
(a) longer
(b) shorter
(c) equal
(d) none of these

Question. In a triangle, the sum of its two sides is ________ third side.
(a) equal to
(b) less than
(c) greater than
(d) none of these

Question. The point of intersection of the angle bisector of all internal angles of a triangle is
(a) orthocentre
(b) incentre
(c) circumcentre
(d) centroid

Question. In fig, PQR is a triangle in which T is a point on QR and if S is a point such that RT = ST: then PQ + PR ___ QS

(a) PQ + PR > QS
(b) PQ + PR < QS
(c) PQ + PR = QS
(d) PQ + PR = 1/2QS

Question. The sum of three altitudes of triangle is ______ the sum of its three sides.
(a) equal to
(b) less than
(c) greater than
(d) none of these

Question. In a right angled triangle, ________ is the longest side.
(a) perpendicular
(b) hypotenuse
(c) base
(d) none of these

Question. In fig, ∠B < ∠A and ∠C < ∠D then relation between AD and BC is

(a) AD > BC
(b) AD < BC
(c) AD = BC
(d) none of these

Question. In a triangle ABC, ∠A = ∠B = 62(1°/2) then the longest side is
(a) AC
(b) BC
(c) AB
(d) none of these

Question. How many equilateral triangles each of 1 cm and fill the given hexagonal rangoli?

(a) 200
(b) 300
(c) 150
(d) 250

Question. How many equilateral triangles each of 1 cm and fill the given star rangoli?
(a) 200
(b) 300
(c) 150
(d) 350

Question. In a triangle ABC, AC > AB and bisector of

(a) acute angle
(b) right angle
(c) obtuse angle
(d) linear angle

Question. The difference between any two sides of a triangle is _____the third side.
(a) equal to
(b) less than
(c) greater than
(d) half

Question. If two angles of a triangle are unequal then the side opposite side to the smaller angle is:
(a) greater
(b) 90⁰
(c) smaller
(d) none of these

Question. The sides opposite to two equal angles of a triangle are:
(a) not equal
(b) congruent
(c) may be congruent
(d) not congruent

Question. Which one of the following is the value of congruency?
(a) SAS
(b) ASS
(c) SSA
(d) none of these

Question. By which congruence rule following triangles are congruent ?
(a) SAS
(b) ASS
(c) AAS
(d) SSS

Question. In a right triangle, if acute angle is double of other angle then hypotenuse is:
(a) equal to the smallest side
(b) three times the smallest side
(c) twice the smallest side
(d) smaller than any of the two sides

Question. In a triangle ABC, if median BE = median CF then triangle is:
(a) Equilateral
(b) Isosceles
(c) Scalene
(d) none of these.

Question. The perimeter of a triangle is _____ the sum of its medians.
(a) equal to
(b) less than
(c) greater than
(d) half of

Question. If one angle of a triangle is equal to the sum of other two angles, then the triangle is
(a) an Equilateral triangle
(b) an Isosceles triangle
(c) an obtuse triangle
(d) a right triangle

Question. In the given figure, the ratio ∠ABD : ∠ACD is

(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) 2 : 3

Question. ∠x and ∠y are exterior angles of a ΔABC, at the points B and C respectively. Also ∠B > ∠C, then relation between ∠x and ∠y is
(a) ∠x > ∠y
(b) ∠x < ∠y
(c) ∠x = ∠y
(d) none of these

Question. In the given figure, PQ > PR, QS and RS are the bisectors of ∠Q and ∠R respectively, then

(a) SQ > SR
(b) SQ < SR
(c) SQ = SR
(d) none of these

Question. If the bisector of vertical angle of a triangle is perpendicular to the base of triangle is
(a) an Equilateral triangle
(b) a scalene triangle
(c) an obtuse angled triangle
(d) an acute angled triangle .

Question. In a ΔABC and ΔPQR, three equality relations between same parts are as follows:
AB = QP, ∠B = ∠P and BC = PR
State which of the congruence conditions applies:
(a) SAS
(b) ASA
(c) SSS
(d) RHS

Question. D, E , F are the midpoints of the sides BC, CA and AB respectively of ∠ABC, then ∠DEF is congruent to triangle
(a) ABC
(b) AEF
(c) BFD, CDE
(d) AFE, BFD, CDE

Question. In quadrilateral ABCD, BM and DN are drawn perpendicular to AC such that BM = DN. If BR = 8 cm, then BD is 

(a) 4 cm
(b) 2 cm
(c) 12 cm
(d) 16 cm

Question. If ΔABC ≅ ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:
(a) BC = PQ
(b) AC = PR
(c) QR = BC
(d) AB = PQ

Question. D is a point on the side BC of a ∠ABC such that AD bisects ΔBAC. Then
(a) BD = CD
(b) BA > BD
(c) BD > BA
(d) CD > CA

Question. Two sides of a triangle are 7 cm and 10 cm.Which of the following length can be the length of the third side?
(A) 19 cm.
(B) 17 cm.
(C) 23 cm.
(D) None of these.

Question. Can 80°, 75° and 20° form a triangle?
(A) Yes
(B) Sometimes
(C) No
(D) None

Question. In the following fig. AB = AC and BD = DC, then

(A) 60°
(B) 120°
(C) 90°
(D) none

Question. In the Fig. given below, find <Z.

(A) 20°
(B) 110°
(C) 45°
(D) None

Question. In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is
(A) 60°
(B) 45°
(C) 30°
(D) 75°

Question.The interior opposite angles of the exterior angle <ACD are

(A) <B, <C
(B) <A, <C
(C) <A, <B
(D) <B, <E

Question. If P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle.
(A) opposite side
(B) one side
(C) between
(D) None

(A) 30°, 60°, 90°

(B) 60°, 36°, 20°

(C) 30°, 90°, 60°

(D) none of these .

 

Question. Two figures are congruent, if they are of the

(A) same shape.

(B) same size.

(C) a & b both.

(D) None.

 

Question. In the given fig., if AD = BC and AD || BC, then

 

(A) AB = AD

(B) AB = DC

(C) BC = CD

(D) none

 

Question. In ΔABC, AB = AC and AD is perpendicular to BC. State the property by which 

(A) SAS property

(B) SSS property

(C) RHS property

(D) None

 

Question. By which congruency property, the two triangles connected by the following figure are congruent.

 

(A) SSA property

(B) SSS property

(C) AAS property

(D) ASA property

 

Question. A, B, C are the three angles of a triangle. If A - B = 35°, B - C = 43° then

(A) 80°, 65°, 35°

(B) 65°, 80°, 35°

(C) 35°, 80°, 65°

(D) None of these.

 

Question. Which of the following statements is not true?

(A) Two line segments having the same length are congruent.

(B) Two squares having the same side length are congruent.

(C) Two circles having the same radius are congruent.

(D) None.

 

Question. E and F are respectively the mid-points of equal sides AB and AC of  ΔABC.Which of the following statement is true?

(A) AB = BC

(B) AE = AC

(C) BF = CE

(D) BC = AF

 

Question. Body

Question. In the adjoining figure

AB||PQ, AC||PR, BC||QR. Then, AP is

 

 

 

Question. Which of the following statements is/are true?

(A) Two triangles having same area are congruent.

(B) If two sides and one angle of a triangle are equal to the corresponding two sides and the angle of another triangle, then the two triangles are congruent.

(C) If the hypotenuse of one right triangle is equal to the hypotenuse of another triangle, then the triangles are congruent.

(D) None.

 

Question. In ΔABC,

 

 

(A) AP, BP, CP

(B) BC,AB,AC

(C) BP, AP, CP

(D) CP, BP, AP

 

Question. In Figure OA = OB and OD = OC.

 

 

Show that

 

 

 

Question.AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

 

 

 

Question. D is a point on side BC of ΔABC such that AD = AC .Show that AB > AD.

 

 

Question. ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that

 

 

Question. ABC and DBC are two isosceles triangles on the same base BC. Show that

 

Question. Angles opposite to equal sides of an isosceles triangle are equal.

 

Question. In Fig, AC = AE, AB = AD and

 

 

 

 

 

Question. In ΔABC, the bisector AD of isosceles.

 

 

 

Question. P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them.

 

 

Question. In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD =AE.

 

 

Question. ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that

Question. AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the erpendicular bisector of AB.

 

Question. When N÷5 leaves a remainder of 2, find the one’s digit of N.

Question. Find the generalised form of 206.

Question. Write the generalised form of a three digit number ‘abc’.

Question. Find the value of A in the addition 

Question. If the division N÷5 leaves a remainder of 1, what will be the ones digits of N?

Question. When N÷2 leaves a remainder of 1, what will be the one’s digit of N?

Question. What will be the unit's digit of N if it is divisible by 5 exactly? 

Question. Check the divisibility of 2147681 by 3. 

Question. If 15Z7 is a multiple of 3 where ‘Z’ is a digit, find the value of Z.

Question. Find the value of Q in the multiplication. 

Question. Find the values of P and Q in the addition. 

Question. The ones digit of a two-digit number is 3 and the sum of digits is 1/7 of the number itself. What is the number?

Question. Find A and B in the addition.

Question. If 42x is a multiple of 3 (where x is a digit), find the value of x.

Question. If 51x3 is a multiple of 9 (where x is a digit), find the value of x.

Question. Find ‘a’ such that the five digit number 91a92 is divisible by 9.

Question. Find a number whose cube is equal to the number itself but its square is not equal to the number itself.

Question. Find two numbers whose product is a one digit number and sum is a two digit number .

Question. A two digit number exceeds the sum of the digits of that number by 18. If the digits at the unit’s place is double the digit in the ten’s place, find the number.

Question. Find A, B, C in the addition. 

Question. In a two digit number the digit in the one's place is three times the digit in the ten's place and the sum of the digits is equal to 12. What is the number?

Question. Fill in the numbers from 7 to 12 (without repetition) so that each side of the given magic triangle adds up to 30. 

Question. The difference between a two digit number and the number obtained by interchanging its digits is 63. What is the difference between the two digits of the number?

Question. Find the values of A and B. 

Question. Find the values of A, B and C in the multiplication. 

Question. If the following three digit numbers are divisible by 3, (i) 223x4 (ii) 4543x (iii) 2562x1 (iv) 3495x then what is the value of x?

Question. Check the divisibility of the following numbers by 9.
(i) 72163458, (ii) 23457891,
(iii) 12304905, (iv)30458091

Question. If the following three digit numbers are divisible by 9,
(i) 23x4 (ii) 543x (iii) 62x1 (iv) 23495x
then what will be the value of x?

Question. In the given triangle, fill in the numbers from 0 to 8 (without repetition) in the circles so that the numbers on each side of a triangle add up to 13. 

Question. Find the value of A, B, C, D and E to complete the number triangle given below. 

Question. In the following, replace A, B, C, D and E by digits to conclude the procedure of division. 

Question. Check the divisibility of 1052896 by 9.

Question. Check the divisibility of 7894561 by 3.

Question.Write the following numbers in generalized form :
a.) 56
b.) 890
c.) 25
d.) 722

Question. If 31y5 is a multiple of 3, where y is a digit, what might be the values of y?

Question. Write the following numbers in the usual form :
a) 4 x 10 + 3
b) 2 x 100 + 9 x 10 + 6
c) 3 x 1000 + 6 x 100 + 0 x 10 + 9

Question. Write the following numbers in generalized form :
a) 22
b) 753
c) 30
d) 861

Question. Fill in the blanks :
a) 5 x 10 + 9 = ______
b) 6 x 1000 + 1 x 100 + 8 x 10 + 7 = ______
c) 7 x 100 + 4 x 10 + 8 = = ______

Question. Write the smallest digit for z so that the following numbers are divisible by 3:
a) 56z89
b) 89z

Question. Without division state whether the given number is divisible by 2:
a) 14567
b) 2248

Question. Check whether the given number is divisible by 6 or not,
a) 2543
b) 3984

Question. Ani and Preeti play a game with numbers. Ani asks Preeti to choose a two-digit number and then to reverse the digits of the number. He then asks her to add both the numbers and divide the answer by 11. Ani guarantees that there will be no remainder. What was the logic behind his guarantee?

Question. Pranay asks Shruti to choose a three-digit number. He then asks her to form two more 3-digit numbers keeping the order of digits same i.e. either clockwise or anti-clockwise. He then asks her to add them up and then divide the resulting answer by 37. He guarantees that there will be no remainder.
What was the logic behind his guarantee?

Question. Find A, B and C in the following : 

Question. Find A and B in the addition : 

Question. Find Q in the addition. 

Question. Find E in the addition. 

Question. Find A, B , C in the addition.