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Maths 3 marks

T2 CH4 Geometry · Tamil Nadu Board STD 6 (Tamil - English Medium). 11 questions.

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11 questions · timed · auto-graded

Question 13 Marks
If one angle of an isosceles triangle is 70°, then find the possibilities for the other two angles
Answer
(i) Given one angle $=70^{\circ}$
Also, it is an isosceles triangle
Another angle also can be $70^{\circ}$
Sum of these two angles $=70^{\circ}+70^{\circ}=140^{\circ}$
We know that the sum of three angles in a triangle $=180^{\circ}$
Third angle $=180^{\circ}-140^{\circ}=40^{\circ}$
One possibility is $70^{\circ}, 70^{\circ}$ and $40^{\circ}$
(ii) Also if one angle is $70^{\circ}$
Sum of other two angles $=180^{\circ}-70^{\circ}=110^{\circ}$
Both are equal
They are $\frac{110}{2}=55^{\circ}$
Another possibility is $70^{\circ}, 55^{\circ}$ and $55^{\circ}$.
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Question 23 Marks
If one angle of an isosceles triangle is 124°, then find the other angles
Answer
In an isosceles triangle, any two sides are equal.
Also, two angles are equal.
Sum of three angles of a triangle $=180^{\circ}$
Given one angle $=124^{\circ}$
Sum of other two angles $=180^{\circ}-124^{\circ}=56^{\circ}$
Other angles are $=\frac{56}{2}=28^{\circ}$
$28^{\circ}$ and $28^{\circ}$.
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Question 33 Marks
What are the angles of an isosceles right angled triangle?
Answer
Since it is a right-angled triangle
One of the angles is $90^{\circ}$
Other two angles are equal because it is an isosceles triangle.
Other two angles must be $45^{\circ}$ and $45^{\circ}$
Angles are $90^{\circ}, 45^{\circ}, 45^{\circ}$.
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Question 43 Marks
Complete the following table:
Types of Triangle/Its Angles Acute angled triangle Right angled triangle Obtuse angled triangle
Any two angles Always acute angles i. Always acute angles
Third angle ii. Right angle iii.
Answer
Types of Triangle/Its Angles Acute angled triangle Right angled triangle Obtuse angled triangle
Any two angles Always acute angles i. Always acute angles Always acute angles
Third angle ii. Acute angle Right angle iii. Obtuse angle
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Question 53 Marks
Two sides of the triangle are given in the table. Find the third side of the triangle.
SI. No. Side - 1 Side - 2 The length of the third side (any three measures)
i. 7 cm 4 cm
ii. 8 cm 8 cm
iii. 7.5 cm 3.5 cm
iv. 10 cm 14 cm
Answer
SI. No. Side - 1 Side - 2 The length of the third side (any three measures)
i. 7 cm 4 cm 8 cm, 9 cm, 10 cm
ii. 8 cm 8 cm 8 cm, 9 cm, 10 cm
iii. 7.5 cm 3.5 cm 5 cm, 6 cm, 7 cm
iv. 10 cm 14 cm 10 cm, 15 cm, 20 cm
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Question 63 Marks
Can a triangle be formed with the following sides? If yes, name the type of triangle.
3.5 cm, 3.5 cm, 3.5 cm
Answer
3.5 cm, 3.5 cm, 3.5 cm
Here sum of two sides = 3.5 cm + 3.5 cm
= 7 cm > 3.5 cm ...(Third side)
∴ Triangle can be formed.
Also, all three sides are equal.
∴ Yes, it is an equilateral triangle.
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Question 73 Marks
Can a triangle be formed with the following sides? If yes, name the type of triangle.
6 cm, 6 cm, 4 cm
Answer
6 cm, 6 cm, 4 cm
Sum of two smaller sides = 4 cm + 6 cm
= 10 cm > 6 cm, third side.
∴ Triangle can be formed.
Also two sides are equal.
∴ Yes, it is an isosceles triangle.
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Question 83 Marks
Can a triangle be formed with the following sides? If yes, name the type of triangle.
10 cm, 8 cm, 5 cm
Answer
10 cm, 8 cm, 5 cm.
Sum of two smaller sides = 8 cm + 5 cm
= 13 cm > 10 cm, third side
∴ Triangle can be formed
None of the sides is equal.
∴ Yes, it is a scalene triangle
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Question 93 Marks
Can a triangle be formed with the following sides? If yes, name the type of triangle.
6.2 cm, 1.3 cm, 3.5 cm
Answer
6.2 cm, 1.3 cm, 3.5 cm.
Here sum of two smaller sides = 1.3 cm + 3.5 cm
= 4.8 cm < 6.2 cm, third side.
∴ No, The triangle cannot be formed
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Question 103 Marks
In ΔABC, name the

a) Three sides: _________, __________, __________
b) Three Angles: _________, __________, __________
c) Three Vertices: _________, __________, __________
Answer
a) Three sides: $\overline{A B}, \overline{B C}, \overline{C A}$
b) Three Angles: $\angle A B C, \angle B C A, \angle C B$ or $\angle A, \angle B, \angle C$
c) Three Vertices: A, B, C
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Question 113 Marks
Using the given information, write the type of triangle in the table given below
S.No ∠1 ∠2 ∠3 Type of triangle based on angles Type of triangle based on sides
i. 60° 40° 80° Acute angled triangle. Scalene Triangle
ii. 50° 50° 80°
iii. 45° 45° 90°
iv. 55° 45° 80°
v. 75° 35° 70°
vi. 60° 30° 90°
vii. 25° 64° 91°
viii. 120° 30° 30°
Answer
S.No ∠1 ∠2 ∠3 Type of triangle based on angles Type of triangle based on sides
i. 60° 40° 80° Acute angled triangle. Scalene Triangle
ii. 50° 50° 80° Acute angled triangle Isosceles triangle
iii. 45° 45° 90° Right−angled triangle Isosceles triangle
iv. 55° 45° 80° Acute angled triangle Scalene triangle
v. 75° 35° 70° Acute angled triangle Scalene triangle
vi. 60° 30° 90° Right−angled triangle Scalene triangle
vii. 25° 64° 91° Obtuse angled triangle Scalene triangle
viii. 120° 30° 30° Obtuse angled triangle Isosceles triangle
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