AP 9th Maths Mock Test 2021 For Chapter 7 - "Triangles" Online Practice Test

1. From the given figure x = .............

150⁰

60⁰

100⁰

120⁰

2. In the given figure the point 'P' bisects AB and DC . Prove that $\triangle$ APC $\cong \triangle$ BPD

a. Consider $\triangle$ APC and $\triangle$ BPD
b. CP = DP
c. AP = BP
d. $\angle$ APC = $\angle$ BPD
e. $\triangle$ APC $\cong \triangle$ BPD
Arrange the steps orderly

a , b , c , d , e

b , c , a , e , d

a , c , d , b , e

a , d , b , c , e

3. Two line segments are congruent if they have same ...............

Shape

Length

Angles

Side

4. Two circles are said to be congruent , if their ....... are equal

Area

Perimeter

Angles

Radii

5. Two rhombuses are said to be congruent if their ......... are equal

One side

One interior angle

Both

Diagonals

6. Any two circles are

Similar

Congruent

Equal

Different

7. Angles opposite to equal sides of a triangle are ...........

Parallel

Unequal

Equal

Similar

8. Each angle of an equilateral triangle is

90⁰

60⁰

45⁰

30⁰

9. An exterior angle of a triangle is equal to the sum of two ............ angles

Interior

Exterior

Interior opposite

Exterior opposite

10. An exterior angle of an isosceles triangle is 110⁰ then the angles in the triangle are ...........

55⁰ , 55⁰ , 70⁰

70⁰ , 70⁰ , 40⁰

Both are possible

Can't find

11. In a triangle ABC , is 2 $\angle$ A = 3 $\angle$ B = 6 $\angle$ C then $\angle$ A , $\angle$ B , $\angle$ C are .............

30⁰ , 60⁰ , 70⁰

90⁰ , 60⁰ , 30⁰

30⁰ , 90⁰ , 60⁰

90⁰ , 30⁰ , 60⁰

12. How many criteria of congruency of triangles are there ?

13. The angles of a triangle are in the ratio 7 : 6 : 2 what is unit place digit of the smallest angle ?

14. Two circles with same radii are ...........

Similar

Congruent

Equal

Different

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

SSA

SAS

ASA

SSS

16. In a triangle , angle opposite to the longer side is ...........

Less

Equal

Half

Greater

17. If $\triangle$ ABC congruent to $\triangle$ DEF under which criteria ?

SSS Congruency

SAS Congruency

ASA Congruency

RHS Congruency

18. AC bisects $\angle$ BAD , $\angle$ BCD which of the following methods can be used to prove $\triangle$ ABC $\cong\triangle$ ADC

SAS

ASA

AAS

There is insufficient information to determine if the triangles are congruent

19. Teacher asked her students to measure the lengths of sides of school garden which is in a triangle shape
Sudha measured as 50 mts , 45 mts and 20 mts
Kiran measured as 40 mts , 20 mts and 60 mts
Radha measured as 45 mts , 20 mts and 50 mts
Jhon measured as 40 mts , 20 mts and 65 mts

Kiran and Radha

Kiran and Jhon

Sudha and Jhon

Sudha and Radha

20. In the given figure AB $\parallel$ CD , AB = CD . $\overline{AC}$ and $\overline{BD}$ intersects at 'O' from the given information which of these is false ?

$\bigtriangleup$ ABC $\cong \bigtriangleup$ BDC

$\angle$ OBA $\cong \angle$ ODC

$\bigtriangleup$ OAB $\cong \bigtriangleup$ OCD

O is the bisecting point of $\overline{AC}$ , $\overline{BD}$

21. $\triangle$ PQR is an equilateral triangle X , Y , Z are the midpoints of the sides and A , B , C are of the midpoints of sides $\triangle$ XYZ , if the perimeter of $\triangle$ PQR is 8.4 cm then perimeter of $\triangle$ ABC =

8.4 cm

2.1 cm

2.8 cm

4.2 cm

22. l , m are two lines intersecting at A , P is a point equidistant . To prove $\overline{AP}$ is the bisector of the angle formed by 'l' and 'm' . Which of the following information is not needed ?

PB = PC

RHS congruency rule

Vertically opposite angles are equal

$\overline{AP}$ is common side

23. From the given figure , what is the additional information needed to prove OBE $\cong \triangle$ OCD ?

BE = CD

BD = CE

$\angle$ OBE = $\angle$ OCD

$\angle$ BOE = $\angle$ COD

24. From a rectangular shape of paper if you cut 3 triangles the area of bigger triangle is

$\frac{1}{4} ^{th}$ area of rectangle

$\frac{3}{4} ^{th}$ area of rectangle

$\frac{1}{2}$ area of rectangle

Equal in areas

25. In $\bigtriangleup$ ABC , $\overline{AD}$ , $\overline{BE}$ are medians $\overline{BE}$ , $\parallel\overline{DF}$ . To prove CF = $\frac{1}{4}$ AC it was written as "In $\bigtriangleup$ ABC , 'D' is the mid - point of $\overline{BC}$ and $\overline{BE}$ , $\parallel\overline{DF}$ . As per triangle mid-point theory 'F' is the mid point of $\overline{CE}$ ,if CF = $\frac{1}{2}$ CE" . Which of the following is the next step ?

CF = $\frac{1}{4}$ AC

2CF = CE

4CF = AC

CF = $\frac{1}{2}$ [ $\frac{1}{2}$ AC]

26. Assertion A : When we have two sides and an angle equal we cannot say that the triangles are congruent unless the angle is between the given sides
Reason R : We can say that the SAS congruency rule holds for the statement

A is correct , R is incorrect

R is correct , A is incorrect

Both A and R are correct but R is not correct explanation of A

Both A and R are correct but R is correct explanation of A

27. Assertion A : The sum of any two sides of a triangle is greater than the third side
Reason R : Sides opposite to equal angles of an isosceles triangle are equal

A is correct , R is incorrect

R is correct , A is incorrect

Both A and R are correct but R is not correct explanation of A

Both A and R are correct but R is correct explanation of A

28. Assertion A : ABC is a right triangle in which $\angle$ A = 90⁰ and AB = AC then $\angle$ B = $\angle$ C
Reason R : Angles opposite to equal sides are equal in a triangle

A is correct , R is incorrect

R is correct , A is incorrect

Both A and R are correct but R is not correct explanation of A

Both A and R are correct but R is correct explanation of A

29. Assertion A : AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD then $\angle$ A > $\angle$ C
Reason R : $\triangle$ ABC is an isosceles triangle in which altitudes BD and CE are drawn to equal sides AC and AB respectively , then these altitudes are equal

A is correct , R is incorrect

R is correct , A is incorrect

Both A and R are correct but R is not correct explanation of A

Both A and R are correct but R is correct explanation of A

30. In the adjacent figure $\triangle$ ABC , D is the midpoint of BC , DE $\bot$ AB , DF $\bot$ AC and DE = DF then ST $\triangle$ BED $\cong\triangle$ CFD then arrange the steps orderly

a. In $\triangle$ ABC , D is a midpoint of BC i.e, BD = DC
b. Consider $\triangle$ BED and $\triangle$ CFD
c. DE = DF
d. $\triangle$ BED $\cong\triangle$ CFD
e. DE $\perp$ AB and DF $\perp$ AC , hence DE = DF
f. BD = DC ; $\angle$ BED = $\angle$ CFD = 90⁰

a , b , c , d , e , f

a , e , b , f , c , d

a , b , e , f , c , d

a , e , f , b , c , d

31. ABC is a right angled triangle in which $\angle$ A = 90⁰ and AB = AC show that $\angle$ B = $\angle$ C
a. Consider $\triangle$ DAC and $\triangle$ DAB
b. Ab = AC , $\angle$ BAD = $\angle$ CAD = 45⁰ , AD = AD
c. Draw AD bisector to $\angle$ BAD
d. $\triangle$ DAC $\cong \triangle$ DAB
e. $\angle$ B = $\angle$ C
Arrange the above steps orderly

a , b , c , d , e

c , a , b , d , e

c , b , a , d , e

c , d , a , b , e

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

a. In $\triangle$ ABD and $\triangle$ ACE
b. AB = AC
c. that is BD = CE
d. $\angle$ B = $\angle$ C
e. Also BE = CD , so BE - DE = CD - DE
f. So $\triangle$ ABD $\cong \triangle$ ACE
g. AB = AE
Arrange the steps orderly

a , b , c , d , e , f , g

a , b , d , e , f , g

a , b , d , c , f , e , g

a , b , c , d , f , g , e

33. Which of the following is different statement ?

8.3 cm , 3.4 cm , 6.1 cm

5.4 cm , 2.3 cm , 3.1 cm

6 cm , 7 cm , 10 cm

3 cm , 5 cm , 5 cm

34. In $\bigtriangleup$ ABC , AB = 5 cm , BC = 6 cm , CA = 7 cm . Identify the relation between the angles

$\angle$ B > $\angle$ A > $\angle$ C

$\angle$ B > $\angle$ C > $\angle$ A

$\angle$ A > $\angle$ B > $\angle$ C

$\angle$ A > $\angle$ C > $\angle$ B

35. If $\triangle$ ABC $\cong \triangle$ DEF , then $\angle$ C =

$\angle$ D

$\angle$ A

$\angle$ E

$\angle$ F

36. $\triangle$ PQR , $\overline{PR}$ is the longest side then the greatest angle is

$\angle$ P

$\angle$ Q

$\angle$ R

90⁰

37. In $\triangle$ XYZ , W is a point on YZ such that XW = XZ then

XY = XW

XY > XW

XY < XW

XY < XZ

38. In the figure , PA = PB and QA = QB then $\angle$ POA is ........... angle

Acute

Obtuse

Right

Reflex

39. In a triangle , if two angles are equal , then sides opposite to them are ...............

Similar

Equal

Congruent

Unequal

40. In a triangle the sides are 6 cm , 8 cm and 10 cm then the greatest angle is .......

100⁰

90⁰

120⁰

60⁰

41. Which of the following is correct ?

A triangle has two right angles

A triangle has two obtuse angles

A triangle has three acute angles

A triangle has one reflex angle

42. Sum of any two sides of a triangle is always ................ third side in a triangle

Equal to

Greater than

Less than

No relation

43. 6 cm , 5 cm , 3 cm form .................. type of triangle

Scalene triangle

Equilateral triangle

Isosceles triangle

Right angled triangle

44. In $\bigtriangleup$ ABC , if $\angle$ A = 45⁰ and $\angle$ B = 70⁰ then the shortest and largest sides of the triangle are ..............

AB , BC

BC , AC

AB , AC

All sides are equal

45. Which of the following statement is correct ?

A triangle cannot have an obtuse angle and a right angle

A triangle cannot have two obtuse angle

The difference of any two sides is less than the third side

All the above

46. In $\bigtriangleup$ ABC , AD $\perp$ BC , $\angle$ B = $\angle$ C and AB = AC , state by which property $\triangle$ ADB $\cong \triangle$ ADC ?

SAS property

SSs property

RHS property

ASA property

47. Which of the following statements are true ?

Two lines segments having the same length are congruent

Two squares having the same side length are congruent

Two circles having the same radius are congruent

All the above

48. Statement : Two triangles are said to be congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other
Reason R : Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other

Statement is false and Reason is true

Statement is true and Reason is false

Both are true

Both are false

49. Statement : If we draw triangles with angles 30⁰ , 70⁰ and 80⁰ and te length of the sides of one triangle be different then that of the corresponding sides of the other then the two triangles are not congruent
Reason R : If two triangles are constructed which have all corresponding angles equal but have a pair of unequal corresponding sides , then the two triangles cannot be congruent to each other

Statement is false and Reason is true

Statement is true and Reason is false

Both are true

Both are false

50. In the figure , diagonal AC of a quadrilateral ABCD bisects the angles A & C then

AB = AD

CB = CD

Both

AB = AC

51. If a triangle is regular then it is .................. triangle

Scalene

Isosceles

Right angle

Equilateral

52. If two isosceles triangles have a common base then the line joining their vertices will

Bisect them at acute angle

Bisect them at right angle

Bisect them at obtuse angle

None

53. The sum of exterior angles of a triangle is

180⁰

360⁰

540⁰

270⁰

54. If in the given diagram BD = AD and AC = CD then $\angle$ CAB : $\angle$ ABD =

3 : 1

1 : 3

1 : 4

4 : 1

55. "In a triangle median divides the triangle into two triangles whose areas are equal " Rough diagram for the above statement is

56. Match the following if $\triangle$ ABC $\cong \triangle$ PQR

ED ( ) P. FD
$\angle$ E ( )Q. $\angle$ D
QR ( )R. PR
$\angle$ R ( )S. $\angle$ P

1-Q , 2-R , 3-S , 4-P

1-P , 2-S , 3-Q , 4-R

1-R , 2-S , 3-P , 4-Q

1-S , 2-P , 3-Q , 4-R

57. ABC is a triangle in which $\angle$ B = 2 $\angle$ C . D is the mid point on BC such that AD bisects $\triangle$ BAC and AB = CD . Based on above data match the following

$\angle$ BAC ( ) a. 36⁰
$\angle$ ACB ( )b.72⁰
$\angle$ ADC ( )c. 108⁰
Exterior of $\angle$ ADB ( )d. 88⁰

1-b , 2-a , 3-c , 4-d

1-b , 2-c , 3-a , 4-d

1-c , 2-a , 3-b , 4-d

1-d , 2-c , 3-a , 4-b

58. A : We can make two different squares with sides having same measure
B : 'Congruent'means equal in all aspects
C : The sides decide the size of the triangle
D : The angle decides the shape of the triangle

A - false and B , C , D - true

A , B - false and C , D - true

A - true and B , C , D - false

A , C - false and B , D - true

59. Statement I : If Ab and CD are intersecting at 'O' then OA = OB and OD = OC then AD $\parallel$ BC
Statement II : PQR is a triangle in which PQ = PR and 'S' is any point on the side PQ , through 'S' . A line is drawn parallel to QR and intersecting PR at 'T' then PS = Qs

I is true , II is false

I is false , II is true

Both are true

Both are false

60. Statement I : In two triangles one of the angle and two sides are equal then the two triangles are congruent
Statement II : In any triangle , the side opposite to the larger angle is shorter
Statement III : The sum of any two sides of a triangle is greater than the third side

I is true , II and III are false

I and III are false , II is true

All are true

II is false and I , III are true

61. i. CPCT are always equal
ii. CPCT means corresponding parts of congruent triangles
iii. CPCT means congruent parts of corresponding triangles
iv. CPCT are related to congruent and similar triangles
Which of the above are correct ?

i , ii , iv

i , iii , iv

i , iii

i , ii

62. i. If one angle , side , angle of two triangles are equal then we say that they are congruent triangles
ii. In right angle triangle if one side and hypotenuse of triangles are equal then we can say that they are congruent
iii. If all sides of a triangle are equal to another triangle then we can say that they are congruent
iv. SSA is a congruency rule
Which of the above are correct ?

i , ii , iv

i , iii , iv

i , iii

i , ii , iii

63. i. In a triangle ABC , exterior angle at A measures 170⁰ and angle at B = 80⁰ then angle at C = 90⁰ii. The sum of three altitudes of a triangle is less than the sum of two sides of a triangle
iii. In a triangle DEF , angle at D is 40⁰ , angle at E is 60⁰ , angle at F is 80⁰ then exterior angle at F is 100⁰iv. In obtuse angled triangle , one of the angle must be > 90⁰ and < 180⁰Which of the above are correct ?

i , ii , iv

i , iii , iv

i , iii

i , ii , iii

64. AB is a line segment and line 'l' is its perpendicular bisector of a point 'P' lies on 'l' Show that 'P' is equidistant from A and B

a. Consider $\triangle$ PCA and $\triangle$ PCB
b. PA = PB as they are corresponding sides of congruent triangles
c. $\triangle$ PCA $\cong \triangle$ PCB
d. AC = BC
e. $\angle$ PCA = $\angle$ PCB = 90⁰f. PC = PC
Arrange the steps orderly

a , b , c , d , e , f

a , d , e , f , c , b

a , e , d , c , f , b

a , d , c , e , b , f

65. Find the odd one

If two triangles have their corresponding sides equal then they are congruent

If two triangles have their corresponding angles equal then they are congruent

If two circles have the same radii then they are congruent

If two squares have the same length of sides , then they are congruent

66. In triangle ABC , if AB > AC then the angle B ...........

> $\angle$ C

> $\angle$ A

< $\angle$ A

< $\angle$ C

67. In $\triangle$ XYZ , XZ is the smallest side , then the smallest angle is ............

$\angle$ X

$\angle$ Y

$\angle$ Z

Can't say

68. The difference of any two sides of a triangle is ....... third side

Greater than

Less than

Equal to

Can't say

69. An exterior angle of a triangle is 120⁰ then the triangle is ...... triangle

Scalene

Isosceles

Equilateral

Right angled

70. If a , b , c are the sides of a triangle then

a - b > c

c > a + b

a + b = c

c < a + b

71. In triangle PQR , QR = 5.4 , $\angle$ P = 50⁰ and $\angle$ Q = 30⁰ then PQ + PR =

9.4

10.2

72. In triangle PQR , QR = 5.4 , $\angle$ P = 50⁰ and $\angle$ Q = 30⁰ then the exterior angle of R =

120⁰

60⁰

80⁰

100⁰

73. In $\triangle$ XYZ , XY = 7 , YZ = 13 and ZX = 12 then the biggest angle is at which vertex ?

None

74. In $\triangle$ ABC , AB = 6.7 , BC = 5.4 , AC = 3.5 and angle at B is 30⁰ , angle at C = 100⁰.In $\triangle$ PQR , QR = 5.4 and angle at p is 50⁰ , angle at Q is 30⁰, From the above data $\triangle$ ABC $\cong \triangle$ PQR under which congruency criterian ?

AAA

SSS

SAS

ASA

75. TQ and TR are angular bisectors of $\angle$ Q and $\angle$ R respectively , the measure of $\angle$ QTR will be

125⁰

100⁰

135⁰

140⁰

76. The value of 'x' from the adjacent figure will be

116⁰

126⁰

108⁰

132⁰

77. In the figure (p+r) =

180⁰

150⁰

280⁰

270⁰

78. If in the given figure angle at p is 130⁰ then the value of x =

60⁰

20⁰

30⁰

40⁰

79. The value of 'q' is

120⁰

80⁰

90⁰

100⁰

80. Which of the following is different ?

4x⁰ = (x + 10)⁰ + (2x + 10)⁰

r = (2x + 10)⁰ + q

4x⁰ + q⁰ = 180⁰

p = (x + 10)⁰ + q

81. In the given triangle is it possible to exist all exterior angles as right angles

Never possible

Sometimes possible

Always possible

There can be 2 right angles

82. ABC is a right angled triangled in which $\angle$ A = 90⁰ and AB = AC then

$\angle$ B < $\angle$ C

$\angle$ B > $\angle$ C

$\angle$ B = $\angle$ C

$\angle$ B $\neq \angle$ C

83. If ABC is isoseles triangle in which AB = AC . Side BA is produced to D such that AD = AB then $\angle$ BCD is a

Acute angle

Obtuse angle

Reflex angle

Right angle

84. Figures which are identical i.e having same shape and size are called

Congruent figures

Congruent

Corresponding angle

None

85. The sum of the three angles of a triangle is

90⁰

180⁰

360⁰

1900⁰

86. In a right angle triangle the 'hypotenuse' is the

Shortest side

Equal to adjacent side

Longest side

Equal to opposite sides

87. The difference of any two sides in a triangle is ............. the third side

Greater than

Less than

Equals

Not equals

88. The sum of any two sides of a triangle is ................ the third side

Less than

Greater than

Equal

Not equal

89. In any triangle , the side opposite to the larger angle is

Longer

Shorter

Equal

None

90. Each angle of an equilateral triangle is

30⁰

60⁰

80⁰

20⁰

91. If two sides of a triangle are unequal , the angle opposite to the longer side is

Shorter

Larger

Either long are short

We can't say

92. Conversely , sides opposite to equal angles of an isosceles triangle are

Equal

Larger than

Smaller than

We can't say

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

Equal

Not equal

No opposite angles

None

94. Congruency of triangles are

95. Congruency of triangles are

SAS

SSS

ASA

All

96. $\cong$ means

Is congruent to

Similar

Equal

Parallel

97. Which of the following is true ?

Two circles are always congruent

Two line segments of same length are always congruent

Two right angle triangles are sometimes congruent

All

98. Which of the following is false ?

Two circles are always congruent

Two line segments of same length are always congruent

Two equilateral triangles with their sides equal are always congruent

All

99. In rhombus , ......... sides are equal

Not equal

100. Which of the following triangle has 60⁰ to each angle ?

None

AP 9th Maths Mock Test 2021 For Chapter 7 – “Triangles” Online Practice Test

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