Mathematics

MCQ | Class 09 | Chapter 7
Triangles

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MCQ | CHAPTER – 7 | CLASS IX
TRIANGLES

Question 1

In triangle ABC, if AB = BC and ∠B = 70°, ∠A will be:

a) 70°                    b) 110°                c) 55°                    d) 130°

Answer: c

Question 2

In given figure, the measure of ∠BAC is

a) 60°                b) 50°                    c) 70°                    d) 80°

Answer (b)

Question 3

For two triangles, if two angles and the
included side of one triangle are equal to two angles and the included side of
another triangle. Then the congruency rule is:

a) SSS            b) ASA                c) SAS                    d) None of the above

Answer: b

Question 4

The angles opposite to equal sides of a
triangle are:

a) Equal

b) Unequal

c) Supplementary angles

d) Complementary angles

Answer: (a)

Question 5

ABC is an isosceles triangle in which
altitudes BE and CF are drawn to equal sides AC and AB, respectively. Then:

a) BE > CF

b) BE < CF

c) BE = CF

d) None of the above

Answer: (c)

Question 6: In a right triangle, the longest side
is:

a) Perpendicular

b) Hypotenuse

c) Base

d) None of the above

Answer: b

Question 7

All the medians of a
triangle are equal in case of a:
a) Scalene triangle

b) Right angled triangle

c) Equilateral triangle

d) Isosceles triangle

Answer
c

Question 8 

If ABC is an equilateral triangle, then
each angle equals to:

a) 90°        b)180°            c) 120°                d) 60°

Answer: d

Question 9

A triangle in which two sides are equal
is called:

a) Scalene triangle

b) Equilateral triangle

c) Isosceles triangle

d) None of the above

Answer: c

Question 10

If AD is an altitude of an isosceles
triangle ABC in which AB = AC. Then:

a) BD = CD

b) BD > CD

c) BD < CD

d) None of the above

Answer: a

Question 11

Which of the following is not a
criterion for congruence of triangles?

a) SAS            b) ASA                c) SSA                d) SSS

Answer: c

Question 12 

In triangle PQR if ∠Q = 90°, then:

a) PQ is the longest side

b) QR is the
longest side

c) PR is
the longest side

d) None of
these

Answer
c

Question 13

In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles
are

a)
Isosceles and congruent

b)
Isosceles but not congruent

c)
Congruent but not isosceles

d) Neither
congruent nor isosceles

Answer: b

Question 14 

If AB = QR, BC = PR and CA = PQ, then

a) ∆ PQR ≅ ∆ BCA

b) ∆ BAC ≅ ∆ RPQ

c) ∆ CBA ≅ ∆ PRQ

d) ∆ ABC ≅ ∆ PQR

Answer: c

Explanation:

Consider two triangles ABC and PQR.

Given that, AB = QR, BC = PR and CA = PQ.

By using Side-Side-Side (SSS rule),

We can say, ∆ CBA ≅ ∆ PRQ

Question 15

In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR =
5 cm. Then the length of PQ is

a) 2 cm               b) 2.5 cm                c) 4 cm                d) 5 cm

Answer: c

Explanation:

Given that, in a triangle PQR, ∠R = ∠P.

Since, ∠R = ∠P, the sides opposite to the equal angles are also equal.

Hence, the length of PQ is 4 cm.

Question 16

If ∆ ABC ≅ ∆ PQR, then which of
the following is not true?

a) AC = PR 

b) BC = PQ

c) QR = BC

d) AB = PQ

Answer: b

Explanation:

Given that, ∆ ABC ≅ ∆ PQR

Hence, AB = PQ

BC = QR

AC =PR

Thus,
BC = PQ is not true, if ∆ ABC ≅ ∆ PQR.

Question 17

In the given figure, if the exterior angle is 135^o then ∠P is:

a) 45^o                b) 60^o                    c) 80^o                        d) 90^o

Answer d

Question 18

In ∆ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to

a) 40°                b) 50°                    c) 80°                    d) 100°

Answer: b 

Explanation: Thus, the given triangle is an isosceles triangle.

By using the angle sum property of a triangle, we get

x + 80°+ x = 180°

2x + 80°= 180°

2x = 180°- 80°

2x = 100°

x = 100°/2 = 50°

Therefore, ∠A = 50°.

Question 19

In a triangle ABC, ∠B = 35° and ∠C = 60°, then

a) ∠A = 80°

b) ∠A = 85°

c) ∠A = 120°

d) ∠A = 145°

Answer b

Question 20

Two sides of a triangle are of lengths 5
cm and 1.5 cm. The length of the third side of the triangle cannot be

a) 3.4 cm            b) 3.6 cm                c) 3.8 cm                    d) 4.1 cm

Answer: a

Explanation: Because In triangle we have following rule for sides

Difference of two sides
< Third side < Sum of two sides

Question 21

In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to

a) 40°            b) 50°                c) 80°                    d) 130°

Answer: b

Question 22 

In ∆ PQR, if ∠R > ∠Q, then

a) QR <
PR 

b) PQ <
PR

c) PQ >
PR

d) QR >
PR 

Answer: c

Question 23 

It is given that ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of
the following is true? 

a) DF = 5
cm, ∠F = 60°

b) DF = 5
cm, ∠E = 60° 

c) DE = 5
cm, ∠E = 60°

d) DE = 5
cm, ∠D = 40

Answer: b

Explanation:

Given that, ∆ ABC ≅ ∆ FDE and AB = 5
cm, ∠B = 40° and ∠A = 80°.

In ∆ ABC,

∠C = 180° – (80°+ 40°)

∠C = 180° – 120°

∠C = 60°

Now : ∆ ABC ≅ ∆ FDE …… Given

By using the CPCT rule, 

AB = DF = 5 cm,

∠C = ∠E = 60°

Hence
correct option is  DF = 5 cm, ∠E = 60°

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