Question Set D

CBSE 9th Standard Mathematics Triangles Sample Question Papers Study Material - QB365

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Questions:

Multiple Choice Question

88 x 1 = 88

In ΔABC, ㄥB = 35°, ㄥC = 65° and the bisector of ㄥBAC meets BC in X.Then, the relation between BX and AX is

(a)

BX = AX

(b)

BX < AX

(c)

BX > AX

(d)

None of these

In ΔABC, AB > AC and D is any point on side BC.Then, the relation between AB and AD is

(a)

AB > AD

(b)

AB = AD

(c)

AB < AD

(d)

None of these

In the following figure, ㄥB > ㄥA and ㄥD > ㄥE.Then, the relation between AE and BD is

(a)

AE = BD

(b)

AE > BD

(c)

AE < BD

(d)

None of these

In the following figure, if AB = AC, then the relation between AB and AD is

(a)

AD = AB

(b)

AD < AB

(c)

AD > AB

(d)

None of these

In ΔABC, ㄥB=30⁰, ㄥC=80⁰ and ㄥA =70⁰ then,

(a)

AB > BC < AC

(b)

AB < BC >AC

(c)

AB > BC > AC

(d)

AB < BC < AC

In ΔABC, if ㄥA > ㄥB > ㄥC then:

(a)

AB > AC

(b)

AC < BC

(c)

AB > BC

(d)

AC > BC

ㄥX and ㄥY are exterior angles of ΔABC at the points B and C respectively. Also ㄥB > ㄥC, then the relation between ㄥXand ㄥYis:

(a)

ㄥX > ㄥY

(b)

ㄥX < ㄥY

(c)

ㄥX = ㄥY

(d)

ㄥX ≥ ㄥY

In the following figure, write the relation between AB and AC.

(a)

AB > AC

(b)

AB < AC

(c)

Ab = AC

(d)

AB=\(1\over2\)AC

For the given triangle PQR, which of the following is true?

(a)

PQ = QR

(b)

PQ > QR

(c)

PQ < QR

(d)

ㄥP = ㄥQ

10.

In ΔPQR, PE is the perpendicular bisector of ㄥQPR, then:

(a)

QE = PE

(b)

QP > QE

(c)

PQ = PR

(d)

PQ > PR

11.

P is a point on side BC of ΔABC such that AP bisects ㄥBAC.Then:

(a)

BP = CP

(b)

BA > BP

(c)

BP > BA

(d)

CP < CA

12.

In ΔABC, ㄥA=100⁰, ㄥB=30⁰ and ㄥC=50⁰, then:

(a)

AB > AC

(b)

BC < AC

(c)

AB < AC

(d)

none of these

13.

If E is a point on side QR of a ΔPQR such that PE bisects ㄥQPR, then:

(a)

QE=ER

(b)

QP > QE

(c)

QE > QP

(d)

ER > RP

14.

In ABC if AB=BC, then:

(a)

ㄥB > ㄥC

(b)

ㄥA=ㄥC

(c)

ㄥA=ㄥB

(d)

ㄥA < ㄥC

15.

If in a triangle XYZ, ㄥY > ㄥX and XZ = 13 em, then XZ is:

(a)

8cm

(b)

9cm

(c)

13.5cm

(d)

13cm

16.

In ΔPQR, if ㄥR > ㄥQ, then:

(a)

QR > PR

(b)

PQ > PR

(c)

PQ < PR

(d)

QR < PR

17.

In ΔABC, if AB > BC then:

(a)

ㄥC < ㄥA

(b)

ㄥC=ㄥA

(c)

ㄥC > ㄥA

(d)

ㄥA=ㄥB

18.

In ΔABC :

(a)

ㄥC > ㄥB

(b)

ㄥB < ㄥA

(c)

ㄥB > ㄥA

(d)

ㄥC > ㄥA

19.

If ΔABC is right angled at B, then:

(a)

AB = AC

(b)

AC < AB

(c)

AB=BC

(d)

AC > Ab

20.

In any triangle ABC, ㄥA > ㄥB and ㄥB > ㄥC, then the smallest side is:

(a)

(b)

(c)

(d)

none of these

21.

It is not possible to construct a triangle when its sides are:

(a)

8.3 em, 3.4 em, 6.1 em

(b)

5.4 em, 2.3 em, 3.1 em

(c)

6 em, 7 em, 10 em

(d)

3 em, 5 em, 5 em

22.

If length of the largest side of a triangle is 12 cm then other two sides can be:

(a)

4.8cm, 8.2cm

(b)

3.2cm, 7.8cm

(c)

6.4cn, 2.8cm

(d)

7.6cm, 3.4cm

23.

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

(a)

3.6cm

(b)

4.5cm

(c)

3.8cm

(d)

3.4cm

24.

Two sides of a triangle are 12 cm and 13 cm.The length of the third side cannot be:

(a)

0.8cm

(b)

5cm

(c)

4cm

(d)

6cm

25.

Two sides of a triangle are of lengths 7 cm and 3.5 em. The length of the third side of the triangle cannot be

(a)

3.6cm

(b)

4.1cm

(c)

3.4cm

(d)

3.8cm

26.

In ΔABC, if ㄥB = ㄥC = 45°, then the longest side is

(a)

(b)

(c)

(d)

none of these

27.

In ΔPQR, ㄥP = 60° and ㄥQ = 50° which side of the' triangle is the longest?

(a)

(b)

(c)

(d)

None

28.

In ΔABC, if ㄥA = 35° and ㄥB = 65°, then the longest side of the triangle is:

(a)

(b)

(c)

(d)

None of these

29.

The sum of the three altitudes of a triangle is the perimeter of the triangle.

(a)

greater than

(b)

equal to

(c)

half of

(d)

less than

30.

In figure, ABCD is a quadrilateral in which AB = BC and AD = DC.Measure of ㄥBCD is:

(a)

150⁰

(b)

30⁰

(c)

105⁰

(d)

72⁰

31.

If the lengths of the perpendiculars drawn from the middle point of a line to the other two sides are equal, then the triangle is:

(a)

equilateral

(b)

isosceles

(c)

equiangular

(d)

scalene.

32.

In the following figure, in ΔABC, AB = AC and AD 丄 BC.Then, side AD is the bisector of

(a)

ㄥA

(b)

side BC

(c)

ㄥA and side BC

(d)

none of these

33.

In figure, if AB = AC and BD = DC, ΔABD and ΔACD are congruent by which criterion.

(a)

SSS

(b)

ASA

(c)

SAS

(d)

RHS

34.

If in two triangles ABC and DEF, AB = DE, BC = EF and AC = DF then Δ ABC ≅ ΔDEF by congruency rule:

(a)

RHS

(b)

SAS

(c)

SSS

(d)

ASA

35.

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

(a)

ΔABC ≅ ΔPQR

(b)

ΔCBA ≅ ΔPRQ

(c)

ΔBAC ≅ ΔRPQ

(d)

ΔPQR ≅ ΔBCA

36.

If ΔABC is congruent to ΔDEF by SSS congruence rule, then:

(a)

ㄥC < ㄥF∆

(b)

ㄥB < ㄥE

(c)

ㄥA < ㄥD

(d)

ㄥA = ㄥD, ㄥB=ㄥE, ㄥC=ㄥF

37.

If ΔABC ≅ DEF by SSS congruence rule then:

(a)

AB = EF, BC = FD, CA = DE

(b)

AB = FD, BC = DE, CA = EF

(c)

AB = DE, BC = EF, CA = FD

(d)

AB = DE, BC = EF, ㄥC = ㄥF

38.

If in two right triangles hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent. This rule is known as:

(a)

SAS congruence rule

(b)

ASA congruence rule

(c)

SSS congruence rule

(d)

RHS congruence rule

39.

If three sides C1fone triangle are equal to three sides of another triangle, then the two triangles are congruent.

(a)

SAS congruence rule

(b)

ASA congruence rule

(c)

AAS congruence rule

(d)

SSS congruence rule.

40.

If the 3 altitudes of a triangle are equal, then triangle is:

(a)

right angled triangle

(b)

isosceles triangle

(c)

acute angled triangle

(d)

equilateral triangle

41.

In an isosceles triangle AB = AC and side BA is extended to D such that AB = AD.Then, the measure of ㄥBCD is:

(a)

70⁰

(b)

90⁰

(c)

60⁰

(d)

45⁰

42.

In figure, if AB = AC and AP = AQ, then by which congruence criterion ΔPBC ≅ ΔlQCB.

(a)

SSS

(b)

ASA

(c)

SAS

(d)

RHS

43.

Which of the following is false?

(a)

The mid-point of the hypotenuse of a right triangle is equidistant from its vertices.

(b)

Each angle of an equilateral triangle is 60°

(c)

The side opposite to the greater angle of a triangle is longer than the side opposite the smaller angle

(d)

The two altitudes corresponding to two equal sides of a triangle are not equal.

44.

In the following figure, BA 丄 AC, DE 丄 EF, BA = DE and BF = DC. Then,

(a)

AC>EF

(b)

AC=EF

(c)

(d)

AC = 2EF

45.

In ΔABC, AB = AC, BD = EC. Then, ΔADE is

(a)

right angled

(b)

scalene

(c)

isosceles

(d)

equilateral

46.

In A ABC, AB = AC and ㄥABD = ㄥACD,then ΔBCD is

(a)

equilateral

(b)

isosceles

(c)

equiangular

(d)

scalene.

47.

In given figure, AD = BC and ㄥBAD = ㄥABC, then ㄥACB equals:

(a)

ㄥABD

(b)

ㄥBAD

(c)

ㄥBDA

(d)

ㄥBAC

48.

In the following figure, ㄥB = ㄥD = 90° and BC = CD.Then, the relation between AB and DE is

(a)

AB = DE

(b)

AB > DE

(c)

AB < DE

(d)

none of these.

49.

In the following figure, in ΔABC, AD = BD and AC = DC and ㄥC = 44°. Then, the measure of ㄥA =

(a)

68⁰

(b)

112⁰

(c)

34⁰

(d)

102⁰

50.

In the following figure, in A ABC, AB = AC; CD = CA and ㄥADC = 20°.Then, ㄥABC=

(a)

10⁰

(b)

20⁰

(c)

30⁰

(d)

40⁰

51.

In triangles ABC and PQR, AB = AC, ㄥC = ㄥPand ㄥB = ㄥQ. The two triangles are:

(a)

isosceles but not congruent

(b)

isosceles and congruent

(c)

congruent but not isosceles

(d)

neither isosceles nor congruent

52.

In the given figure, AD is the median, then ΔBAD is
∵

(a)

55⁰

(b)

50⁰

(c)

100⁰

(d)

40⁰

53.

In ΔABC and ΔFDE, if AB = DF, BC = DE, AC = EF and ㄥD = 550 Then, ㄥB=

(a)

55⁰

(b)

35⁰

(c)

90⁰

(d)

45⁰

54.

In ΔABC, ㄥC = ㄥA and BC = 6 ern and AC = 5 cm, then the length of AB is:

(a)

6 cm

(b)

5cm

(c)

3cm

(d)

2.5cm

55.

ΔABC is an isosceles right angled triangle in which ㄥA = 90⁰, then ㄥB =

(a)

60⁰

(b)

90⁰

(c)

45⁰

(d)

30⁰

56.

In ΔPQR, PQ = PR and ㄥQ = 65⁰, then ㄥP is :

(a)

55⁰

(b)

130⁰

(c)

65⁰

(d)

50⁰

57.

In figure, in ΔABC, AB = AC. The value of x is:

(a)

80⁰

(b)

100⁰

(c)

130⁰

(d)

120⁰

58.

In figure, if AB = AC find x.

(a)

55⁰

(b)

55⁰

(c)

50⁰

(d)

70⁰

59.

In ΔABC, BC = AB and L B = 80⁰, then ㄥA is equal to:

(a)

80⁰

(b)

40⁰

(c)

50⁰

(d)

180⁰

60.

The measure of each angle of an equilateral triangle is

(a)

30⁰

(b)

45⁰

(c)

60⁰

(d)

90⁰

61.

In ΔABC and ΔPQR, AB = PR and ㄥA = ㄥP. The two triangles will be congruent by SAS axiom if:

(a)

BC = QR

(b)

AC = PQ

(c)

AC = QR

(d)

BC = PR

62.

In ΔABC and ΔDEF, AB = DF and ㄥA = ㄥD.The two triangles will be congruent by SAS axiom if:

(a)

BC = EF

(b)

AC = DE

(c)

DC = DE

(d)

AC = EF

63.

In triangles ABC and DEF, AB = DE, BC = EF and ㄥA = ㄥ D. Are the triangles congruent? If yes, by which congruency rule?

(a)

yes, by SAS

(b)

(c)

yes, by SSS

(d)

yes, by RHS

64.

In ΔAOC and ΔXYZ, ㄥA=ㄥX, AO=XZ, AC-XY then by which congruence rule ΔAOC≌ΔXYZ?

(a)

SAS

(b)

ASA

(c)

SSS

(d)

RHS

65.

Given ΔOAP ≌ ΔOBP in figure, the criteria by which the triangles are congruent:

(a)

SAS

(b)

SSS

(c)

RHS

(d)

ASA

66.

In the given figure, if AB = DC, ㄥABD = ㄥCDB, which congruence rule would you apply to prove ΔABD ≅ CDB?

(a)

SAS

(b)

SSS

(c)

AAS

(d)

SAS

67.

Which congruence rule is used to show ΔACB ≅ ADB?

(a)

ASA

(b)

SSS

(c)

AAS

(d)

SAS

68.

In two triangles ABC and DEF, ㄥA = ㄥD, ㄥB = ㄥE and AB = EF, then are the two triangles congruent? If yes, by which congruency rule?

(a)

yes, by AA

(b)

(c)

yes, by ASA

(d)

Yes, by RHS

69.

Among the following which is not a criteria for congruence of two triangles?

(a)

SAS

(b)

ASA

(c)

SSA

(d)

SSS

70.

In the given figure, OA = OB, OD = OC, then ΔAOD ≌ BOC by congruency rule:

(a)

SAS

(b)

ASA

(c)

SAS

(d)

RHS

71.

Two triangles are congruent, if any two pairs of angles and one pair of corresponding sides are equal. This rule is known as

(a)

SAS congruence rule

(b)

ASA congruence rule

(c)

AAS congruence rule

(d)

SSS congruence rule

72.

Two triangles are congruent, if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. This rule is known as

(a)

SAS congruence rule

(b)

ASA congruence rule

(c)

SSS congruence rule

(d)

AAS congruence rule.

73.

Two triangles are congruent, if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle. This rule is known as

(a)

SAS congruence rule

(b)

ASA congruence rule

(c)

SSS congruence rule

(d)

RHS congruence rule.

74.

ΔABC ≅ ΔPQR.If AB = 5cm, ㄥB = 40⁰and ㄥA = 80⁰, then which of the following is true?

(a)

QP = 5cm, ㄥP = 60⁰

(b)

QP = 5cm, ㄥR = 60⁰

(c)

QR = 5cm, ㄥR = 60⁰

(d)

QR = 5cm, ㄥQ = 40⁰

75.

ΔABC ≌ ΔPQR, then which of the following is true:

(a)

A↔R

(b)

AB=QR

(c)

AC=PQ

(d)

AB=PQ

76.

Two equilateral triangles are congruent when:

(a)

their angles ar equal

(b)

their sides are equal

(c)

their sides are proportional

(d)

their areas are proportional

77.

If the side of a square is a cm, what is the side of a congruent square?

(a)

1 cm

(b)

2 cm

(c)

a cm

(d)

2a cm

78.

If the diameter of a circle is 2cm, what is the diameter of circle congruent to it?

(a)

1 cm

(b)

2 cm

(c)

3 cm

(d)

4 cm

79.

Two circles are congruent.If the diameter of one circle is 2cm, then the radius of the other circle is

(a)

1 cm

(b)

2 cm

(c)

3 cm

(d)

4 cm

80.

Two circles are congruent.If the radius of one circle is 1cm, then the diameter of the other circle is

(a)

1 cm

(b)

2 cm

(c)

4 cm

(d)

0.5 cm

81.

Two circles are congruent.If the radius of one circle is 3cm, what is the radius of the other circle?

(a)

3 cm

(b)

6 cm

(c)

1.5 cm

(d)

1 cm

82.

The side of an equilateral triangle is 4cm.An equilateral triangle, congruent to it, has the side length

(a)

1 cm

(b)

2 cm

(c)

3 cm

(d)

4 cm

83.

The symbol for correspondence is

(a)

⟶

(b)

⇔

(c)

↔

(d)

≡

84.

The symbol for congruence is

(a)

(b)

(c)

⁰

(d)

≅

85.

A triangle has

(a)

6 angles

(b)

5 angles

(c)

8 angles

(d)

3 angles

86.

A triangle has

(a)

2 verticles

(b)

3 verticles

(c)

4 verticles

(d)

5 verticles

87.

'Tri' means

(a)

one

(b)

two

(c)

three

(d)

four

88.

A closed figure formed by three intersecting lines is called

(a)

circle

(b)

square

(c)

triangle

(d)

rhombus

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Answers Key:

Multiple Choice Question

88 x 1 = 88

ㄥBAC=180⁰-(35⁰+65⁰)=80⁰
ㄥBAX=40⁰
ㄥBAX > ㄥABX
BX > AX

AB > AC
ㄥACB > ㄥABC
ㄥADB > ㄥACB
ㄥADB > ㄥABC
AB > AD

ㄥB > ㄥA
AC > BC
ㄥD > ㄥE
CE > CD
Adding (1) and (2)
AC+CE > BC+CD
⇒ AE > BD

AB=AC
ㄥABC = ㄥACB
Each is an acute angle
ㄥACD is an obtuse angle
ㄥACD > ㄥADC
AD > AC
But AB=AC
AD > AB

ㄥA > ㄥA
AB > AC ......(1)
ㄥA > ㄥB
BC > AC .......(2)
In view of (1) and (2), AB > BC > AC

ㄥA > ㄥB > ㄥC
BC > AC

(b)
ㄥX < ㄥY

ㄥABC=180⁰-135⁰=45⁰
ㄥACB=180⁰-115⁰=65⁰
ㄥACB > ㄥABC
AB > AC

ㄥPQR=180⁰-100⁰=80⁰
ㄥQPR = 180⁰-125⁰=55⁰
ㄥP+ㄥQ+ㄥR=180⁰
⇒ 55⁰+80⁰+ㄥR=180⁰
⇒ ㄥR=45⁰
ㄥP > ㄥR
QR > PQ
⇒ PQ < PQ

10.

11.

(b)
BA > BP

12.

<C > <B
AB > AC

13.

(b)
QP > QE

14.

AB=BC
ㄥC=ㄥA

15.

ㄥY > ㄥX
XZ > YZ
⇒ XZ > 13cm

16.

ㄥR > ㄥQ
PQ > PR

17.

AB > BC
ㄥC > ㄥA

18.

BC > AC > AB
ㄥA > ㄥB
⇒ ㄥB < ㄥA

19.

ㄥB > ㄥC
∴ AC > AB

20.

ㄥA > ㄥB
BC > CA
ㄥB > ㄥC
CA > AB
BC > CA > AB
AB is the smallest side

21.

2.3 + 3.1 = 5.4
The construction of triangle is not possible

22.

The sum of the lengths of any two sides of a triangle is always greater than the third side Here, 4.8 + 8.2 = 13 em > 12 cm

23.

The sum of the lengths of any two sides of a triangle is greater than the third side 3.4 + 1.5 = 4.9 < 5

24.

The difference of the lengths of any two sides of a triangle is always smaller than the length of the third side.Here, 13 - 12 = 1, 1> 0.8.

25.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

26.

ㄥA=90⁰ ∴ BC is the longest side

27.

ㄥP+ㄥQ+ㄥR=180⁰
⇒ 60⁰+50⁰+ㄥR=180⁰
⇒ ㄥR=70⁰
∵ ㄥR > ㄥP
∴ PQ > QR
∵ ㄥR > ㄥQ
∴ PQ > PR
In view of (1) and (2), PQ is the longest side

28.

ㄥA+ㄥB+ㄥC=180⁰
⇒ 35⁰+65⁰+ㄥC=180⁰
⇒ ㄥC=180⁰
∵ ㄥC > ㄥA
∵ AB > BC
∵ ㄥC > ㄥB
∴ AB > AC
In view of (1) and (2), AB is the longest side.

29.

Theorem

30.

31.

(b)
isosceles

32.

ΔADB ≅ ΔADC
∴ ㄥDAB = ㄥDAC

33.

AB=AC
BD=CD
AD=AD
ΔABD ≅ ΔACD

34.

Obvious

35.

AB=QR
BC=PR=RP
CA=PQ
∴ A ↔ Q
B ↔ R
C ↔ P
∴ ΔCBA ≅ ΔPRQ

36.

(d)
ㄥA = ㄥD, ㄥB=ㄥE, ㄥC=ㄥF

37.

38.

Theorem

39.

Theorem

40.

(d)
equilateral triangle

41.

(b)
90⁰

42.

43.

(d) is false

44.

(b)
AC=EF

45.

46.

(b)
isosceles

47.

48.

ㄥCBA=ㄥCDE=90⁰
ㄥACB=ㄥECD
BC=CD
∴ ΔCBA≅ΔCDE
∴ AB=DE

49.

(d)
102⁰

50.

(d)
40⁰

51.

(a)
isosceles but not congruent

52.

(b)
50⁰

53.

(b)
35⁰

54.

(a)
6 cm

55.

56.

(d)
50⁰

57.

58.

(d)
70⁰

59.

ㄥA+ㄥB+ㄥC=180⁰
⇒ ㄥA+80⁰+ㄥC=180⁰
⇒ ㄥA+ㄥC=100⁰
∵ BC=AB
∴ ㄥA=ㄥC
| Angles opposite to equal sides of a triangle are equal

60.

61.

(b)
AC = PQ

62.

(b)
AC = DE

63.

This is Ass which is not a congruency rule.So, No

64.

Obvious

65.

(a)
SAS

66.

(a)
SAS

67.

(d)
SAS

68.

69.

70.

In ΔAOD and ΔBOC
OA=OB
OD=OC
ㄥAOD=ㄥBOC
∴ ΔAOD≅ΔBOC

71.

Theorem

72.

Theorem

73.

Theorem

74.

(b)
QP = 5cm, ㄥR = 60⁰

75.

Obviously AB=PQ

76.

Obviously(b)

77.

Two squares of the same side length ar congruent

78.

Two circles of the same radii are congruent

79.

Two circles of the same radii are congruent

80.

Two circles of the same radii are congruent

81.

Two circles of the same radii are congruent

82.

Two equilateral triangles of the same side length are congruent

83.

↔ denotes correspondence

84.

≌ represents congruence.

85.

(d)
3 angles

86.

(b)
3 verticles

87.

88.

CBSE 9th Standard Mathematics Triangles Sample Question Papers Study Material - QB365 Set D

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chapter: Triangles - Sample Question Papers

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