Exercise 4.7 - Chapter 4 Geometry 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

$\mathbf{E x} 4.7$
Multiple Choice Questions :
Question 1.
The exterior angle of a triangle is equal to the sum of two
(1) Exterior angles
(2) Interior opposite angles
(3) Alternate angles
(4) Interior angles
Hint: Exterior angle $=180^{\circ}$ - Interior angle $=$ sum of interior opposite angle Solution:
(2) Interior opposite angles
 

Question $2 .$
In the quadrilateral $\mathrm{ABCD}, \mathrm{AB}=\mathrm{BC}$ and $\mathrm{AD}=\mathrm{DC}$ Measure of $\angle \mathrm{BCD}$ is

(1) $150^{\circ}$
(2) $30^{\circ}$
(3) $105^{\circ}$
(4) $72^{\circ}$

Solution:
(3) $105^{\circ}$

Question $3 .$
$\mathrm{ABCD}$ is a square, diagonals $\mathrm{AC}$ and $\mathrm{BD}$ meet at $\mathrm{O}$. The number of pairs of congruent triangles are

(1) 6
(2) 8
(3) 4
(4) 12
Solution:
(1) 6

Question $4 .$
In the given figure $C E \| D B$ then the value of $x^{\circ}$ is

(1) $45^{\circ}$
(2) $30^{\circ}$
(3) $75^{\circ}$
(4) $85^{\circ}$
Hint: $35^{2}+x^{2}+60^{\circ}=180^{2} \Rightarrow x=8 y^{2}$
Solution:
(4) $85^{\circ}$

Question $5 .$
The correct statement out of the following is

(1) $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$
(2) $\triangle \mathrm{ABC} \cong \triangle \mathrm{DFE}$
(3) $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$
(4) $\triangle \mathrm{ABC} \cong \triangle \mathrm{FED}$
Hint: $\angle \mathrm{C}=\angle \mathrm{D} ; \angle \mathrm{B}=\mathrm{E} ; \angle \mathrm{A}=\angle \mathrm{F}$
Solution:
(4) $\triangle \mathrm{ABC}=\triangle \mathrm{FED}$
 

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 $\angle A$ and $\angle B$ of a quadrilateral $A B C D$ meet at $O$, then $\angle A O B$ is
(1) $\angle \mathrm{C}+\angle \mathrm{D}$
(2) $\frac{1}{2}(\angle C+\angle D)$
(3) $\frac{1}{2} \angle \mathrm{C}+\frac{1}{3} \angle \mathrm{D}$
(4) $\frac{1}{3} \angle \mathrm{C}+\frac{1}{2} \angle \mathrm{D}$
Hint:
$\angle \mathrm{AOB}=180-\frac{1}{2}(\angle \mathrm{A}+\angle \mathrm{B})=\frac{360-(\angle \mathrm{A}+\mathrm{B})}{2}=\frac{1}{2}(\angle \mathrm{C}+\angle \mathrm{D})$

Solution:
(2) $\frac{1}{2}(\angle \mathbf{C}+\angle \mathbf{D})$
 

Question $8 .$
The interior angle made by the side in a parallelogram is $90^{\circ}$ then the parallelogram is a
(1) rhombus
(2) rectangle
(3) trapezium
(4) Kite
Hint:
If one angle of a parallelogram is $90^{\circ}$, 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 $3 x-40, x+20$ and $2 x-10$ then the value of $x$ is
(1) $40^{\circ}$

(2) $35^{\circ}$
(3) $50^{\circ}$
(4) $45^{\circ}$
Hint: $3 x-40+x+20+2 x-10-180^{\circ} \Rightarrow 6 x=210 \Rightarrow x=35^{\circ}$
Solution:
(2) 35

Question $11 .$
$P Q$ and RS are two equal chords of a circle with centre $O$ such that $\angle P O Q=70^{\circ}$, then $O R S=$
(1) $60^{\circ}$
(2) $70^{\circ}$
(3) $55^{\circ}$
(4) $80^{\circ}$
Solution:
(3) $55^{\circ}$

Question $12 .$
A chord is at a distance of $15 \mathrm{~cm}$ from the centre of the circle of radius $25 \mathrm{~cm}$. The length of the chord is
(1) $25 \mathrm{~cm}$
(2) $20 \mathrm{~cm}$
(3) $40 \mathrm{~cm}$
(4) $18 \mathrm{~cm}$

Solution:
(3) $40 \mathrm{~cm}$

Question $13 .$
In the figure, $\mathrm{O}$ is the centre of the circle and $\angle \mathrm{ACB}=40^{\circ}$ then $\angle \mathrm{AOB}=$
(1) $80^{\circ}$
(2) $85^{\circ}$
(3) $70^{\circ}$
(4) $65^{\circ}$

Solution:
(1) $80^{\circ}$

Question $14 .$
In a cyclic quadrilaterals $\mathrm{ABCD}, \angle \mathrm{A}=4 \mathrm{x}, \angle \mathrm{C}=2 \mathrm{x}$ the value of $\mathrm{x}$ is
(1) $30^{\circ}$
(2) $20^{\circ}$
(3) $15^{\circ}$
(4) $25^{\circ}$

Solution:
(1) $30^{\circ}$

Question $15 .$
In the figure, $\mathrm{O}$ is the centre of a circle and diameter $\mathrm{AB}$ bisects the chord $\mathrm{CD}$ at a point $\mathrm{E}$ such that $\mathrm{CE}=$ $\mathrm{ED}=8 \mathrm{~cm}$ and $\mathrm{EB}=4 \mathrm{~cm}$. The radius of the circle is
(1) $8 \mathrm{~cm}$
(2) $4 \mathrm{~cm}$
(3) $6 \mathrm{~cm}$
(4) $10 \mathrm{~cm}$

Solution:
(4) $10 \mathrm{~cm}$

Question $16 .$
In the figure, PQRS and PTVS are two cyclic quadrilaterals, if $\angle \mathrm{QRS}=80^{\circ}$, then $\angle \mathrm{TVS}=$
(1) $80^{\circ}$
(2) $100^{\circ}$
(3) $70^{\circ}$
(4) $90^{\circ}$

Solution:
(1) $80^{\circ}$
 

Question $17 .$
If one angle of a cyclic quadrilateral is $75^{\circ}$, then the opposite angle is
(1) $100^{\circ}$
(2) $105^{\circ}$
(3) $85^{\circ}$
(4) $90^{\circ}$
Hint: $180^{\circ}-75^{\circ}=105^{\circ}$
Solution:
(2) $105^{\circ}$

Question $18 .$
In the figure, $\mathrm{ABCD}$ is a cyclic quadrilateral in which $\mathrm{DC}$ produced to $\mathrm{E}$ and $\mathrm{CF}$ is drawn parallel to $\mathrm{AB}$ such that $\angle A D C=80^{\circ}$ and $\angle E C F=20^{\circ}$, then $\angle B A D=$ ?
(1) $100^{\circ}$
(2) $20^{\circ}$
(3) $120^{\circ}$
(4) $110^{\circ}$

Solution:
(3) $120^{\circ}$

Question $19 .$
$\mathrm{AD}$ is a diameter of a circle and $\mathrm{AB}$ is a chord. If $\mathrm{AD}=30 \mathrm{~cm}$ and $\mathrm{AB}=24 \mathrm{~cm}$ then the distance of $\mathrm{AB}$ from the centre of the circle is
(1) $10 \mathrm{~cm}$
(2) $9 \mathrm{~cm}$
(3) $8 \mathrm{~cm}$
(4) $6 \mathrm{~cm}$

Solution

(2) 9 cm

Question $20 .$
In the given figure, If $\mathrm{OP}=17 \mathrm{~cm} \mathrm{PQ}=30 \mathrm{~cm}$ and $\mathrm{OS}$ is perpendicular to $\mathrm{PQ}$, then $\mathrm{RS}$ is
(1) $10 \mathrm{~cm}$
(2) $6 \mathrm{~cm}$
(3) $7 \mathrm{~cm}$
(4) $9 \mathrm{~cm}$

Solution:
(4) $9 \mathrm{~cm}$