6th Maths : Term 2 Unit 4 : Geometry : Text Book Back Exercises Questions with Answers, Solution

**Exercise
4.1**

** **

**1. Fill in the blanks:**

a) Every triangle has at least ** two** acute angles.

b) A triangle in which none of the sides equal is
called a ** Scalene triangle**.

c) In an isosceles triangle ** two** angles are equal.

d) The sum of three angles of a triangle is ** 180°**.

e) A right angled triangle with two equal sides
is called ** Isosceles right angled
triangle**.

** **

**2. Match the following:**

(i) No sides are equal − Isosceles triangle

(ii) One right angle − Scalene triangle

(iii) One obtuse angle − Right angled triangle

(iv) Two sides of equal length − Equilateral triangle

(v) All sides are equal − Obtuse angled triangle

**Answer **

(i) No sides are equal − Scalene triangle

(ii) One right angle − Right angled triangle

(iii) One obtuse angle − Obtuse angled triangle

(iv) Two sides of equal length − Isosceles triangle

(v) All sides are equal − Equilateral triangle

**3.
In ΔABC, name the **

** a) Three sides: ______ , ______ , _______**

**b)
Three Angles: ______ , ______ , _______ **

**c)
Three Vertices: ______ , _______ , _______**

a) Three sides :

b) Three Angles : __∠____ABC__**, **__∠____BCA__**, **__∠____CAB__

c) Three Vertices : __A,__ __B,__ __C__

** **

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

**Answer:**

(i) Equilateral triangle

(ii) Scalene triangle

(iii) Isoceles triangle

(iv) Scalene triangle

** **

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

**Answer:**

(i) Acute angled
triangle

(ii) Right angled
triangle

(iii) Obtuse angled
triangle

(iv) Acute angled
triangle

** **

**6.
Classify the following triangles based on its sides and angles.**

**Answer:**

(i) Isoceles acute
angled triangle

(ii) Scalene right
angled triangle

(iii) Isoceles obtuse
angled triangle

(iv) Isoceles right
angled triangle

(v) Equilateral acute
angled triangle

(vi) Scalene obtuse
angled triangle

** **

**7.
Can a triangle be formed with the following sides? If yes, name the type of triangle.**

**(i)
8 cm, 6 cm, 4 cm**

**(ii)
10 cm, 8 cm, 5 cm**

**(iii)
6.2 cm, 1.3 cm, 3.5 cm **

**(iv)
6 cm, 6 cm, 4 cm**

**(v)
3.5 cm, 3.5 cm, 3.5 cm**

** (vi) 9 cm,
4 cm, 5 cm**

**(i) 8 cm, 6 cm, 4 cm**

The sum of two smaller sides = 6 + 4 = 10 cm > 8 cm, the
third side.

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is scalene triangle.

**(ii) 10 cm, 8 cm, 5 cm**

The sum of two smaller sides = 8 + 5 = 13 cm > 10 cm, the
third side.

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is scalene triangle.

**(iii) 6.2 cm, 1.3 cm, 3.5 cm**

The sum of two smaller sides = 1.3 + 3.5 = 4.8 cm < 6.2 cm the
third side.

The sum of two smaller sides is lesser than the third side.

So, a triangle can not be formed with the given sides.

**(iv) 6 cm, 6 cm, 4 cm**

The sum of two smaller sides = 6 + 4=10 cm > 6 cm, the third
side

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

It is Isosceles triangle.

**(v) 3.5 cm, 3.5 cm, 3.5 cm**

The three sides are equal, so definitely a triangle can be
formed, as the triangle in equality is satisfied. It is equilateral triangle.

**(vi) 9 cm, 4 cm, 5 cm**

The sum of two smaller sides = 4 + 5 = 9 cm, the third side.

The sum of two smaller sides is not greater than the third side.

So, a triangle can not be formed with the given sides.

** **

**8.
Can a triangle be formed with the following angles? If yes, name the type of triangle.**

**(i)
60° , 60° , 60° **

**(ii)
90° , 55° , 35° **

**(iii)
60° , 40° , 42° **

**(iv)
60° , 90° , 90° **

**(v)
70° , 60° , 50°**

**(vi)
100° , 50° , 30°**

**(i) 60°, 60°, 60°**

The sum of three angles = 60° + 60° + 60° = 180°

So, a triangle can be formed with the given angles.

It is acute angled triangle.

**(ii) 90°, 55°, 35°**

The sum of three angles = 90° + 55° + 35° = 180°

So, a triangle can be formed with the given angles.

It is right angled triangle.

**(iii) 60°, 40°, 42°**

The sum of three angles = 60° + 40° + 42° = 142° ≠ 180°

So, a triangle can not be formed with the given angles.

**(iv) 60°, 90°, 90°**

The sum of three angles = 60° + 90° + 92° = 240° ≠ 180°

So, a triangle can not be formed with the given angles.

**(v) 70°, 60°, 50°**

The sum of three angles = 70° + 60° + 50° = 180°

So, a triangle can be formed with the given angles.

It is acute angled triangle.

**(vi) 100°, 50°, 30°**

The sum of three angles = 100° + 50° + 30° = 180°

So, a triangle can be formed with the given angles.

It is obtuse angled triangle.

** **

**9.
Two angles of the triangles are given. Find the third angle.**

**(i)
80° , 60° **

**(ii)
75° , 35° **

**(iii)
52° , 68° **

**(iv)
50° , 90° **

**(v)
120° , 30°**

**(vi)
55° , 85°**

**(i) 80°, 60°**

**The two angles 80°, 60°**

The sum of three angles = 180°

The sum of two angles = 80° + 60° = 140°

The third angle = The sum of three angles − The sum of two
angles

= 180°− 140° = 40°

**(ii) 75°, 35°**

**The two angles 75°, 35°**

The sum of three angles = 180°

The sum of two angles = 75° + 35° = 110°

The third angle = The sum of three angles − The sum of two
angles

= 180°− 110° = 70°

**(iii) 52°, 68°**

**The two angles 52°, 68°**

The sum of three angles = 180°

The sum of two angles = 52° + 68° = 120°

The third angle = The sum of three angles − The sum of two
angles

= 180°− 120° = 60°

**(iv) 50°, 90°**

**The two angles 50°, 90°**

The sum of three angles = 180°

The sum of two angles = 50° + 90° = 140°

The third angle = The sum of three angles − The sum of two
angles

= 180°− 140° = 40°

**(v) 120°, 30°**

**The two angles 120°, 30°**

The sum of three angles = 180°

The sum of two angles = 120° + 30° = 150°

The third angle = The sum of three angles − The sum of two
angles

= 180° − 150° = 30°

**(vi) 55°, 85°**

**The two angles 55°, 85°**

The sum of three angles = 180°

The sum of two angles = 55° + 85° = 140°

The third angle = The sum of three angles − The sum of two
angles

= 180° − 140° = 40°

** **

**10.
I am a closed figure with each of my three angles is 60° . Who am I?**

I am an equilateral
triangle.

** **

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

**Answer:**

** **

__Objective
Type Questions__

**12.
The given triangle is _______. **

a) a right angled triangle

b) an equilateral triangle

c) a scalene triangle

d) an obtuse angled triangle

*Answer:***b) an equilateral triangle**

**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

*Answer:***d) an acute angled triangle**

**14.
If two sides of a triangle are 5 cm and
9 cm, then the third side is _______.**

a) 5 *cm*

b) 3 *cm*

c) 4 *cm*

d) 14 *cm*

*Answer:***a) 5 cm**

**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

*Answer:***d) acute, acute, right**

**16.
An equilateral triangle is **

a) an obtuse angled triangle

b) a right angled triangle

c) an acute angled triangle

d) a scalene triangle

*Answer:***c) an acute angled triangle**

** **

__ANSWERS: __

__Exercise 4.1 __

**1. a) two b)
scalene triangle c) two d) 180° e) isosceles right angled triangle**

**2. i) Scalene
triangle**

**ii) Right angled
triangle**

**iii) Obtuse angled
triangle**

**iv) Isosceles
triangle**

**v) Equilateral
triangle**

**3. a) **

**b) ****∠****ABC, ****∠****BCA, ****∠****CAB or ****∠****A, ****∠****B, ****∠****C**

**c) A, B, C**

**4. i) Equilateral
triangle ii) Scalene triangle iii) Isosceles triangle iv) Scalene triangle**

**5. i) Acute angled
triangle**

**ii) Right angled
triangle**

**iii) Obtuse angled
triangle**

**iv) Acute angled
triangle**

**6. i) a) Isosceles
Acute angled triangle**

**ii) a) Scalene
Right -angled triangle**

**iii) a) Isosceles
Obtuse angled triangle**

**iv) a) Isosceles
Right -angled triangle**

**v) a) Equilateral
Acute angled triangle**

**vi) a) Scalene
Obtuse angled triangle**

**7. i) Yes, Scalene
triangle**

**ii) Yes, Scalene
triangle**

**iii) No, The
triangle cannot be formed**

**iv) Yes, Isosceles
triangle**

**v) Yes, Equilateral
triangle**

**vi) No, The
triangle cannot be formed**

**8. i) Yes, Acute
angled triangle**

**ii) Yes, Right
angled triangle**

**iii) No, The
triangle cannot be formed**

**iv) No, The
triangle cannot be formed**

**v) Yes, Acute
angled triangle**

**vi) Yes, Obtuse
angled triangle**

**9. i) 40° ii) 70°
iii) 60° iv) 40° v) 30° vi) 40°**

**10. Equilateral
Triangle**

**11. ii) Acute angled
triangle, Isosceles triangle**

**iii) Right angled
triangle, Isosceles triangle**

**iv) Acute angled
triangle, Scalene triangle**

**v) Acute angled
triangle, Scalene triangle**

**vi) Right angled
triangle, Scalene triangle**

**vii) Obtuse angled
triangle, Scalene triangle**

**viii) Obtuse angled
triangle, Isosceles triangle**

**Objective Type
Questions**

**12. b **

**13. d **

**14. a **

**15. d **

**16. c**

Tags : Questions with Answers, Solution | Geometry | Term 2 Chapter 4 | 6th Maths , 6th Maths : Term 2 Unit 4 : Geometry

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6th Maths : Term 2 Unit 4 : Geometry : Exercise 4.1 | Questions with Answers, Solution | Geometry | Term 2 Chapter 4 | 6th Maths

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