Chapter: 6th Maths : Term 2 Unit 4 : Geometry
Exercise 4.1
1. Fill in the blanks:
Answer:
3. Components of a Triangle:
Objective Type Questions
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:
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.
| (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 |
(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
(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
In ΔABC, name the:
4. Classification by Sides:
a) Three sides : AB, BC, CA
b) Three Angles : ∠ABC, ∠BCA, ∠CAB (or ∠A, ∠B, ∠C)
c) Three Vertices : A, B, C
b) Three Angles : ∠ABC, ∠BCA, ∠CAB (or ∠A, ∠B, ∠C)
c) Three Vertices : A, B, C
Classify the given triangles based on its sides as scalene, isosceles or equilateral.
5. Classification by Angles:
(i) Equilateral triangle
(ii) Scalene triangle
(iii) Isosceles triangle
(iv) Scalene triangle
(ii) Scalene triangle
(iii) Isosceles triangle
(iv) Scalene triangle
Classify the given triangles based on its angles as acute angled, right angled or obtuse angled.
6. Two-way Classification:
(i) Acute angled triangle
(ii) Right angled triangle
(iii) Obtuse angled triangle
(iv) Acute angled triangle
(ii) Right angled triangle
(iii) Obtuse angled triangle
(iv) Acute angled triangle
Classify the following triangles based on its sides and angles.
7. Triangle Inequality Check:
(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
(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
Can a triangle be formed with the following sides? If yes, name the type of triangle.
8. Angle Sum Check:
(i) 8 cm, 6 cm, 4 cm: Yes (6+4=10>8), Scalene triangle.
(ii) 10 cm, 8 cm, 5 cm: Yes (8+5=13>10), Scalene triangle.
(iii) 6.2 cm, 1.3 cm, 3.5 cm: No (1.3+3.5=4.8 < 6.2).
(iv) 6 cm, 6 cm, 4 cm: Yes (6+4=10>6), Isosceles triangle.
(v) 3.5 cm, 3.5 cm, 3.5 cm: Yes, Equilateral triangle.
(vi) 9 cm, 4 cm, 5 cm: No (4+5=9, not greater than 9).
(ii) 10 cm, 8 cm, 5 cm: Yes (8+5=13>10), Scalene triangle.
(iii) 6.2 cm, 1.3 cm, 3.5 cm: No (1.3+3.5=4.8 < 6.2).
(iv) 6 cm, 6 cm, 4 cm: Yes (6+4=10>6), Isosceles triangle.
(v) 3.5 cm, 3.5 cm, 3.5 cm: Yes, Equilateral triangle.
(vi) 9 cm, 4 cm, 5 cm: No (4+5=9, not greater than 9).
Can a triangle be formed with the following angles? If yes, name the type.
9. Missing Angle Calculation:
(i) 60°, 60°, 60°: Yes (Sum=180°), Acute angled triangle.
(ii) 90°, 55°, 35°: Yes (Sum=180°), Right angled triangle.
(iii) 60°, 40°, 42°: No (Sum=142°).
(iv) 60°, 90°, 90°: No (Sum=240°).
(v) 70°, 60°, 50°: Yes (Sum=180°), Acute angled triangle.
(vi) 100°, 50°, 30°: Yes (Sum=180°), Obtuse angled triangle.
(ii) 90°, 55°, 35°: Yes (Sum=180°), Right angled triangle.
(iii) 60°, 40°, 42°: No (Sum=142°).
(iv) 60°, 90°, 90°: No (Sum=240°).
(v) 70°, 60°, 50°: Yes (Sum=180°), Acute angled triangle.
(vi) 100°, 50°, 30°: Yes (Sum=180°), Obtuse angled triangle.
Two angles are given. Find the third angle.
(i) 80°, 60°: 180° - 140° = 40°
(ii) 75°, 35°: 180° - 110° = 70°
(iii) 52°, 68°: 180° - 120° = 60°
(iv) 50°, 90°: 180° - 140° = 40°
(v) 120°, 30°: 180° - 150° = 30°
(vi) 55°, 85°: 180° - 140° = 40°
(ii) 75°, 35°: 180° - 110° = 70°
(iii) 52°, 68°: 180° - 120° = 60°
(iv) 50°, 90°: 180° - 140° = 40°
(v) 120°, 30°: 180° - 150° = 30°
(vi) 55°, 85°: 180° - 140° = 40°
10. I am a closed figure with each of my three angles is 60° . Who am I?
11. Information Table:
I am an equilateral triangle.
12. The given triangle is _______.
a) right angled triangle | b) equilateral triangle | c) scalene triangle | d) 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) obtuse angled | b) right angled | c) isosceles right angled | d) acute angled
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) obtuse angled | b) right angled | c) acute angled | d) scalene triangle
Answer: c) an acute angled triangle
ANSWERS Summary: Exercise 4.1
1. a) two | b) scalene | c) two | d) 180° | e) isosceles right angled
2. i) Scalene | ii) Right angled | iii) Obtuse angled | iv) Isosceles | v) Equilateral
4. i) Equilateral | ii) Scalene | iii) Isosceles | iv) Scalene
5. i) Acute | ii) Right | iii) Obtuse | iv) Acute
7. i) Yes, Scalene | ii) Yes, Scalene | iii) No | iv) Yes, Isosceles | v) Yes, Equilateral | vi) No
8. i) Yes, Acute | ii) Yes, Right | iii) No | iv) No | v) Yes, Acute | vi) Yes, Obtuse
12. b | 13. d | 14. a | 15. d | 16. c