RS AGGARWAL CLASS 9 CHAPTER 9 CONGRUENCE OF TRIANGLES AND INEQUALITIES IN A TRIANGLE MCQ

 MULTIPLE CHOICE QUESTIONS

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Question 1:

Which of the following is not a criterion for congruence of triangles?
(a) SSA
(b) SAS
(c) ASA
(d) SSS

Answer 1:

(a) SSA
SSA is not a criterion for congruence of triangles.

Question 2:

If AB = QR, BC = RP and CA = PQ, then which of the following holds?
(a) ABC ≅ ∆PQR
(b) CBA ≅ ∆PQR
(c) CAB ≅ ∆PQR
(d) BCA ≅ ∆PQR

Answer 2:

(c) CABPQR
As,
AB = QR,   (given)
BC = RP,     (given)
CA = PQ     (given)


CABPQR

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Question 3:

If ABC ≅ ∆PQR  then which of the following is not true?
(a) BC = PQ
(b) AC = PR
(c) BC = QR
(d) AB = PQ

Answer 3:

(a) BC = PQ

If , then
BC = QR
Hence, the correct answer is option (a).

Question 4:

In ABC, AB = AC and ∠B = 50°. Then, ∠A = ?
(a) 40°
(b) 50°
(c) 80°
(d) 130°

Answer 4:

In , we have:
AB = AC 
B = 50°
Since ABC is an isosceles triangle, we have:


In triangle ABC, we have:

Hence, the correct answer is option (c).

Question 5:

In ABC, BC = AB and ∠B = 80°. Then, ∠A = ?
(a) 50°
(b) 40°
(c) 100°
(d) 80°

 

Answer 5:

Given: In ABCBC AB and ∠B = 80°. 

In ABC,

As, 



Let 

Using angle sum property of a triangle,





Hence, the correct option is (a).

Question 6:

In ABC, ∠C = ∠A, BC = 4 cm and AC = 5 cm. Then, AB = ?
(a) 4 cm
(b) 5 cm
(c) 8 cm
(d) 2.5 cm

Answer 6:










Given: In ABC, ∠C = ∠A, BC = 4 cm and AC = 5 cm.

In ABC,

As, ∠C = ∠A                   (Given)

Therefore,        (Sides opposite to equal angles.)



Hence, the correct option is (a).

Question 7:

Two sides of a triangle are of length 4 cm and 2.5 cm. The length of the third side of the triangle cannot be
(a) 6 cm
(b) 6.5 cm
(c) 5.5 cm
(d) 6.3 cn

Answer 7:

Since, 4 + 2.5 = 6.5

So, 6.5 cm cannot be the third side of the triangle, as the sum of two sides of a triangle is always greater than the third side.

Hence, the correct option is (b).

Question 8:

In ABC, if ∠C > ∠B, then
(a) BC > AC
(b) AB > AC

(c) AB > AC
(d) BC > AC








Answer 8:

(b) AB > AC

In ABC, we have:
C>B
The side opposite to the greater angle is larger.
AB>AC

Question 9:

It is given that ABC ≅ ∆ FDE in which AB = 5 cm, ∠B = 40°, A = 80° and FD = 5 cm. Then, which of the following is true?
(a) ∠D = 60°
(b) ∠E = 60°

(c) ∠F = 60°
(d) D = 80°

Answer 9:

(b)​ E=60°

ABCFDE
AB = 5cm, B=40°,A=80° and FD = 5cm

Then A+B+C=180°80°+40°+C=180°C=60°Also, C=E
E=60°

Question 10:

In ABC, ∠A = 40° and ∠B = 60°. Then the longest side of ∆ABC is
(a) BC
(b) AC
(c) AB
(d) cannot be determined

Answer 10:

(c) AB

In triangle ABC, we have:
A=40°,B=60°        ...(Given)
Here, A+B+C=180°60°+40°+C=180°C=80°
∴ The side opposite toC, i.e., AB, is the longest side of triangle ABC.

Question 11:

In the given figure, AB > AC. Then which of the following is true?
(a) AB < AD
(b) AB = AD
(c) AB > AD
(d) Cannot be determined

Answer 11:

(c) AB > AD

AB>AC is given.

ACB>ABC

 Now, ADB>ACD    (exterior angle)ADB>ACB>ABCADB>ABDAB>AD

Question 12:

In the given figure, AB > AC. If BO and CO are the bisectors of B and ∠C respectively, then
(a) OB = OC
(b) OB > OC
(c) OB < OC










Answer 12:

(b) OB > OC

AB >AC    (Given)
C>B
12C>12B
OCB>OBC  (Given)
OB>OC

Question 13:

In the given figure, AB = AC and OB = OC. Then, ABO : ∠ACO = ?
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) None of these










Answer 13:

(a) 1:1

​In OAB and OAC, we have:
AB=AC   (Given)OB=OC    (Given) OA =OA    (Common side)
Thus, OABOAC     (SSS criterion)
i.e., ABO=ACO
∴ ABO : ACO=1 : 1

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Question 14:

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is
(a) equilateral
(b) isosceles
(c) scalene
(d) right-angled

Answer 14:

(b) isosceles


In ABC, BLAC.
CMAB such that BL=CM.

To prove: AB = AC

In ABL and ACM,BL=CM     (Given)BAL=CAM     (Common angle)ALB=AMC      (Each 90°)ABLACM   (AAS criterion) AB=AC   (CPCT)



Question 15:

In ∆ABC and ∆DEF, it is given that AB = DE and BC = EF. In order that ∆ABC ≅ ∆DEF, we must have
(a) A = ∠D
(b) ∠B = ∠E
(c) ∠C = ∠F
(d) none of these

Answer 15:


(b) B=E


In ABC and DEF, we have:
AB = DE      (Given)
BC = EF       (Given)
In order that ABCDEF, we must have B=E.



Question 16:

In ABC and ∆DEF, it is given that ∠B = ∠E and ∠C = ∠F. In order that ∆ABC ≅ ∆DEF, we must have
(a) AB = DF
(b) AC = DE
(c) BC = EF
(d) ∠A = ∠D

Answer 16:






In order that ABCDEF, we must have BC = EF.
Hence, the correct answer is option (c).

Question 17:

In ABC and ∆PQR, it is given that AB = AC, ∠C = ∠P and ∠B = ∠Q. Then, the two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but not isosceles
(d) neither congruent nor isosceles










Answer 17:

(a) isosceles but not congruent

AB =AC C=BP=Q        [C=P and B=Q]
Thus, both the triangles are isosceles but not congruent.

Question 18:

Which is true?
(a) A triangle can have two right angles.
(b) A triangle can have two obtuse angles.
(c) A triangle can have two acute angles.
(d) An exterior angle of a triangle is less than either of the interior opposite angles.










Answer 18:

(c) A triangle can have two acute angles.
The sum of two acute angles is always less than 180o, thus satisfying the angle sum property of a triangle.
Therefore, a triangle can have two acute angles.

Question 19:

Fill in the blanks with < or >.
(a) (Sum of any two sides of a triangle) ...... (the third side)
(b) (Difference of any two sides of a triangle) ...... (the third side)
(c) (Sum of three altitudes of a triangle) ...... (sum of its three side)
(d) (Sum of any two sides of a triangle) ...... (twice the median to the 3rd side)
(e) (Perimenter of a triangle) ...... (sum of its three medians)

Answer 19:


a) Sum of any two sides of a triangle > the third side

b) Difference of any two sides of a triangle < the third side

c) Sum of three altitudes of a triangle < sum of its three side

d) Sum of any two sides of a triangle > twice the median to the 3rd side

e) Perimeter of a triangle > sum of its three medians

Question 20:

Fill in the blanks.
(a) Each angle of an equilateral triangle measures ...... .
(b) Medians of an equilateral triangle are ...... .
(c) In a right triangle the hypotenuse is the ...... side.
(d) Drawing a ABC with AB = 3 cm, BC = 4 cm and CA = 7 cm is ...... .

Answer 20:

a) Each angle of an equilateral triangle measures 60°.

b) Medians of an equilateral triangle are equal.

c) In a right triangle, the hypotenuse is the longest side.

d) Drawing a ABC with AB = 3cm, BC = 4cm and CA = 7cm is not possible.

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