Exercise 4.1 - Chapter 4 Geometry Term 2 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex 4.1
Question $1 .$
Fill in the blanks.
(a) Every triangle has at least ___ acute angles.
(b) A triangle in which none of the sides equal is called a
(c) In an isosceles triangle angles are equal.
(d) The sum of three angles of a triangle is
(c) A right-angled triangle with two equal sides is called
Solution:
(a) Two
(b) Scalene Triangle
(c) Two
(d) $180^{\circ}$
(c) Isosceles right-angled triangle

Question $2 .$
Match the following:

Solution:

Question $3 .$
In $\triangle \mathrm{ABC}$, name the
(a) Three sides:
(b) Three Angles:
(c) Three Vertices:

Solution:

(a) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CA}}$
(b) $\angle \mathrm{ABC}, \angle \mathrm{BCA}, \angle \mathrm{CAB}$ or $\angle \mathrm{A}, \angle \mathrm{B}, \angle \mathrm{C}$
(c) $\mathrm{A}, \mathrm{B}, \mathrm{C}$

Question $4 .$
Classify the given triangles based on its sides as scalene, isosceles or equilateral.

Solution:
(i) Equilateral Triangle
(ii) Scalene Triangle
(iii) Isosceles Triangle
(iv) Scalene Triangle

Question $5 .$
Classify the given triangles based on its angles as acute-angled, right-angled or obtuse-angled.

Solution:
(i) Isosceles Acute angled triangle
(ii) Scalene Right angled triangle
(iii) Isosceles Obtuse angled triangle
(iv) Isosceles Right angled triangle
(v) Equilateral Acute angled triangle
(vi) Scalene Obtuse angled triangle

Question 7 .
Can a triangle be formed with the following sides? If yes, name the type of triangle.
(i) $8 \mathrm{~cm}, 6 \mathrm{~cm}, 4 \mathrm{~cm}$
(ii) $10 \mathrm{~cm}, 8 \mathrm{~cm}, 5 \mathrm{~cm}$
(iii) $6.2 \mathrm{~cm}, 1.3 \mathrm{~cm}, 3.5 \mathrm{~cm}$
(iv) $6 \mathrm{~cm}, 6 \mathrm{~cm}, 4 \mathrm{~cm}$
(v) $3.5 \mathrm{~cm}, 3.5 \mathrm{~cm}, 3.5 \mathrm{~cm}$
(vi) $9 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$
Solution:
(i) Sum of two smaller sides of the triangle
$=6+4=10 \mathrm{~cm}>8 \mathrm{~cm}$
It is greater than the third side. So, a triangle can be formed scalene triangle.
(ii) Sum of two smaller sides of the triangle
$=8+5=13 \mathrm{~cm}>10 \mathrm{~cm}$
It is greater than the third side. So, a triangle can be formed scalene triangle.

(iii) Sum of two smaller sides of the triangle
$=1.3+3.5=4.8 \mathrm{~cm}<6.2 \mathrm{~cm}$
It is not greater than the third side. So, a triangle cannot be formed.
(iv) Two sides are equal.
So, a triangle can be formed. Isosceles triangle.
(v) Three sides are equal.
So, a triangle can be formed equilateral triangle.
(vi) Sum of two smaller sides of the triangle
$=1+5=9 \mathrm{~cm}=9 \mathrm{~cm}$
It is equal to the third side. No, a triangle cannot be formed.

Question 8 .
Can a triangle be formed with the following angles? if yes, name the type of triangle.
(i) $60^{\circ}, 60^{\circ}, 60^{\circ}$
(ii) $90^{\circ}, 55^{\circ}, 35^{\circ}$
(iii) $60^{\circ}, 40^{\circ}, 42^{\circ}$
(iv) $60^{\circ}, 90^{\circ}, 90^{\circ}$
(v) $70^{\circ}, 60^{\circ}, 50^{\circ}$
(vi) $100^{\circ}, 50^{\circ}, 30^{\circ}$
Solution:
(i) $60^{\circ}, 60^{\circ}, 60^{\circ}$
Sum of three angles $=60^{\circ}+60^{\circ}+60^{\circ}=180^{\circ}$
Yes, a triangle can be formed.
$\therefore$ It is Acute angled triangle. [ $\because$ all the angles $<90^{\circ}$ ]
(ii) $90^{\circ}, 55^{\circ}, 35^{\circ} .$
Sum of three angles $=90^{\circ}+55^{\circ}+55^{\circ}=180^{\circ}$
Yes, a triangle can be formed.
$\therefore$ It is a right-angled triangle, [ $\because$ one angle is $90^{\circ}$ ]
(iii) $60^{\circ}, 40^{\circ}, 42^{\circ} .$
Sum of three angles $=60^{\circ}+40^{\circ}+42^{\circ}=142^{\circ} \neq 180^{\circ}$
No, The triangle cannot be formed.

(iv) $60^{\circ}, 90^{\circ}, 90^{\circ}$.
Sum of three angles $=60^{\circ}+90^{\circ}+90^{\circ}=240^{\circ} \neq 180^{\circ}$
$\therefore$ No. The triangle cannot be formed. [ $\because$ one angle is $>90^{\circ}$ ]
(v) $70^{\circ}, 60^{\circ}, 50^{\circ}$.
Sum of three angles $=70^{\circ}+60^{\circ}+50^{\circ}=180^{\circ}$
Yes, A triangle can be formed.
$\therefore$ It is an acute-angled triangle.
(vi) $100^{\circ}, 50^{\circ}, 30^{\circ}$.
Sum of three angles $=100^{\circ}+50^{\circ}+30^{\circ}=180^{\circ}$
Yes, A triangle can be formed.
$\therefore$ It is an obtuse-angled triangle.

Question $9 .$
Two angles of the triangles are given. Find the third angle.
(i) $80^{\circ}, 60^{\circ}$
(ii) $52^{\circ}, 68^{\circ}$
(iii) $75^{\circ}, 35^{\circ}$
(iv) $50^{\circ}, 90^{\circ}$
(v) $120^{\circ}, 30^{\circ}$
(vi) $55^{\circ}, 85^{\circ}$
Solution:
(i) $80^{\circ}, 60^{\circ}$
Let the third angle be $x$.
Sum of the angles $=180^{\circ}$
$80^{\circ}+60^{\circ}+\mathrm{x}=180^{\circ}$
$140+x=180^{\circ}$
$x=180^{\circ}-140^{\circ}$
$\mathrm{x}=40^{\circ}$
Third angle $=40^{\circ}$

(ii) $52^{\circ}, 68^{\circ}$
Let the third angle be $x$.
Sum of the angles $=180^{\circ}$
$52^{\circ}+68^{\circ}+x=180^{\circ}$
$120+\mathrm{x}=180^{\circ}$
$180^{\circ}-120^{\circ}$
$\mathrm{x}=60^{\circ}$
Third angle $=60^{\circ}$
(iii) $75^{\circ}, 35^{\circ}$
Let the third angle be $x$.
Sum of the angles $180^{\circ}$
$75^{\circ}+35^{\circ}+x=180^{\circ}$
$110+x=180^{\circ}$
$x=180^{\circ}-110^{\circ}$
$\mathrm{x}=70^{\circ}$
Third angle $=70^{\circ}$
(iv) $50^{\circ}, 90^{\circ}$
Let the third angle be $x$. Sum of the angles $=180^{\circ}$
$50^{\circ}+90^{\circ}+x=180^{\circ}$
$140+x=180^{\circ}$
$\mathrm{x}=180^{\circ}-140^{\circ}$
$\mathrm{x}=40^{\circ}$
Third angle $=40^{\circ}$

(v) $120^{\circ}, 30^{\circ}$
Let the third angle be $x$.
Sum of the angles $=180^{\circ}$
$120^{\circ}+30^{\circ}+x=180^{\circ}$
$150+x=180^{\circ}$
$x=180^{\circ}-150^{\circ}$
$x=30^{\circ}$
Third angle $=30^{\circ}$
(vi) $55^{\circ}, 85^{\circ}$
Let the third angle be $\mathrm{X}$.
Sum of the angles $=180^{\circ}$
$55^{\circ}+85^{\circ}+x=180^{\circ}$
$140+x=180^{\circ}$
$x=180^{\circ}-140^{\circ}$
$x=40^{\circ}$
Third angle $=40^{\circ}$
 

Question $10 .$
I am a closed figure with each of my three angles is $60^{\circ}$. Who am I?
Solution:
Equilateral Triangle.
 

Question $11 .$
Using the given information, write the type of triangle in the table given below.

Solution:

Objective Type Questions
Question 12 .
The given triangle is

(a) a right angled triangle
(b) an equilateral triangle
(c) a scalene triangle
(d) an obtuse angled triangle
Solution:
(b) an equilateral triangle
 

Question $13 .$
If all angles of a triangle are less than a right angle, then it is called ...........
(a) an obtuse angled triangle
(b) a right angled triangle
(c) an isosceles right angled triangle
(d) an acute angled triangle
Solution:
(d) an acute angled triangle

Question $14 .$
If two sides of a triangle are $5 \mathrm{~cm}$ and $9 \mathrm{~cm}$ then the third side is
(a) $5 \mathrm{~cm}$
(b) $3 \mathrm{~cm}$
(c) $4 \mathrm{~cm}$
(d) $14 \mathrm{~cm}$
Solution:
(a) $5 \mathrm{~cm}$

Question $15 .$
The angles of a right angled triangle are
(a) acute, acute, obtuse
(b) acute, right, right
(c) right, obtuse, acute
(d) acute, acute, right
Solution:
(d) acute, acute, right
 

Question $16 .$
An equilateral triangle is
(a) an obtuse-angled triangle
(b) a right-angled triangle
(c) an acute-angled triangle
(d) scalene triangle
Solution:
(c) an acute-angled triangle