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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 4 Geometry Ex 4.7

Multiple Choice Questions :

Question 1.
The exterior angle of a triangle is equal to the sum of two
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 1
(1) Exterior angles
(2) Interior opposite angles
(3) Alternate angles
(4) Interior angles
Hint: Exterior angle = 180°- Interior angle = sum of interior opposite angle
Solution:
(2) Interior opposite angles

Question 2.
In the quadrilateral ABCD, AB = BC and AD = DC Measure of ∠BCD is
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 2
(1) 150°
(2) 30°
(3) 105°
(4) 72°
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 3
Solution:
(3) 105°

Question 3.
ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles are
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 4
(1) 6
(2) 8
(3) 4
(4) 12
Solution:
(1) 6

Question 4.
In the given figure CE || DB then the value of x° is
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 5
(1) 45°
(2) 30°
(3) 75°
(4) 85°
Hint: 35° + x°+ 60° = 180° ⇒ x = 85°
Solution:
(4) 85°

Question 5.
The correct statement out of the following is
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 6
(1) ∆ABC ≅ ∆DEF
(2) ∆ABC ≅ ∆DFE
(3) ∆ABC ≅ ∆FDE
(4) ∆ABC ≅ ∆FED
Hint: ∠C = ∠D; ∠B = E; ∠A = ∠F
Solution:
(4) ∆ABC = ∆FED

Question 6.
If the diagonal of a rhombus are equal, then the rhombus is a
(1) Parallelogram but not a rectangle
(2) Rectangle but not a square
(3) Square
(4) Parallelogram but not a square
Solution:
(3) Square

Question 7.
If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 7
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 8
Solution:
(2) \(\frac{1}{2}(\angle \mathbf{C}+\angle \mathbf{D})\)

Question 8.
The interior angle made by the side in a parallelogram is 90° then the parallelogram
is a Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 9
(1) rhombus
(2) rectangle
(3) trapezium
(4) Kite
Hint:
If one angle of a parallelogram is 90°, then it is a rectangle
Solution:
(2) rectangle

Question 9.
Which of the following statement is correct?
(1) Opposite angles of a parallelogram are not equal.
(2) Adjacent angles of a parallelogram are complementary.
(3) Diagonals of a parallelogram are always equal.
(4) Both pairs of opposite side of a parallelogram are always equal.
Hint:
Opposite sides of a parallelogram are equal.
Solution:
(4) Both pairs of opposite side of a parallelogram are always equal

Question 10.
The angles of the triangle are 3x – 40, x + 20 and 2x – 10 then the value of x is
(1) 40°
(2) 35°
(3) 50°
(4) 45°
Hint: 3x – 40 + x + 20 + 2x- 10 – 180° ⇒ 6x = 210 ⇒ x = 35°
Solution:
(2) 35

Question 11.
PQ and RS are two equal chords of a circle with centre O such that ∠POQ = 70°, then ORS =
(1) 60°
(2) 70°
(3) 55°
(4) 80°
Solution:
(3) 55°
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 50

Question 12.
A chord is at a distance of 15cm from the centre of the circle of radius 25cm. The length of the chord is
(1) 25 cm
(2) 20 cm
(3) 40 cm
(4) 18 cm
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 51
Solution:
(3) 40 cm

Question 13.
In the figure, O is the centre of the circle and ∠ACB = 40° then ∠AOB =
(1) 80°
(2) 85°
(3) 70°
(4) 65°
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 52
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 53
Solution:
(1) 80°

Question 14.
In a cyclic quadrilaterals ABCD, ∠A = 4x, ∠C = 2x the value of x is
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 54
(1) 30°
(2) 20°
(3) 15°
(4) 25°
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 55
Solution:
(1) 30°

Question 15.
In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is
(1) 8 cm
(2) 4 cm
(3) 6 cm
(4) 10 cm
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 56
Solution:
(4) 10 cm

Question 16.
In the figure, PQRS and PTVS are two cyclic quadrilaterals, if ∠QRS = 80°, then ∠TVS =
(1) 80°
(2) 100°
(3) 70°
(4) 90°
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 57
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 58
Solution:
(1) 80°

Question 17.
If one angle of a cyclic quadrilateral is 75°, then the opposite angle is
(1) 100°
(2) 105°
(3) 85°
(4) 90°
Hint: 180° – 75° =105°
Solution:
(2) 105°

Question 18.
In the figure, ABCD is a cyclic quadrilateral in which DC produced to E and CF is drawn parallel to AB such that ∠ADC = 80° and ∠ECF = 20°, then ∠BAD = ?
(1) 100°
(2) 20°
(3) 120°
(4) 110°
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 59
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 81
Solution:
(3) 120°

Question 19.
AD is a diameter of a circle and AB is a chord. If AD = 30 cm and AB = 24 cm then the distance of AB from the centre of the circle is
(1) 10 cm
(2) 9 cm
(3) 8 cm
(4) 6 cm
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 61

Question 20.
In the given figure, If OP = 17cm PQ = 30 cm and OS is perpendicular to PQ, then RS is
(1) 10 cm
(2) 6 cm
(3) 7 cm
(4) 9 cm
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 63
Hint:
Samacheer Kalvi 9th Maths Chapter 4 Geometry Ex 4.7 64
Solution:
(4) 9 cm

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