CBSE Class 6 Mathematics Understanding Elementary Shapes Worksheet Set 02

Question. In a \( \Delta\text{ABC} \), \( \text{AB} = 12\text{ cm} \), \( \text{BC} = 13\text{ cm} \), \( \text{AC} = 5\text{ cm} \) and \( \angle\text{C} = 90^\circ \). Classify the triangle according to sides and angle.
Answer:
• Classification according to sides: Since all three sides are of different lengths (\( \text{AB} \neq \text{BC} \neq \text{AC} \)), it is a Scalene triangle.
• Classification according to angle: Since one angle is a right angle (\( \angle\text{C} = 90^\circ \)), it is a Right-angled triangle.
Therefore, \( \Delta\text{ABC} \) is a Right-angled scalene triangle.

Question. State the following as true or false .Correct the statement if false.
(a) An obtuse angle is \( < 90^\circ \).
(b) A measure of a complete angle is \( 360^\circ \).
(c) Straight angle lies between one fourth and half of a revolution.
Answer:
(a) False. Correct statement: An obtuse angle is greater than \( 90^\circ \) and less than \( 180^\circ \) (an angle less than \( 90^\circ \) is an acute angle).
(b) True. The measure of a complete angle is \( 360^\circ \).
(c) False. Correct statement: A straight angle is equal to half of a revolution (\( 180^\circ \)), whereas an angle that lies between one-fourth and half of a revolution is an obtuse angle.

Question. If \( \text{BD} = 2\text{BA} + \text{AD} \), \( \text{LM} = 3\text{LP} - \text{PM} \) and \( \text{BA} = 3\text{ cm} \), \( \text{AD} = 2.5\text{ cm} \), \( \text{LP} = 4\text{ cm} \) and \( \text{PM} = 1.5\text{ cm} \), find which is one is greater BD or LM?
Answer:
Calculating the value of \( \text{BD} \):
\[ \text{BD} = 2(3\text{ cm}) + 2.5\text{ cm} = 6\text{ cm} + 2.5\text{ cm} = 8.5\text{ cm} \]
Calculating the value of \( \text{LM} \):
\[ \text{LM} = 3(4\text{ cm}) - 1.5\text{ cm} = 12\text{ cm} - 1.5\text{ cm} = 10.5\text{ cm} \]
Comparing the two lengths:
\( 10.5\text{ cm} > 8.5\text{ cm} \implies \text{LM} > \text{BD} \)
Therefore, LM is greater.

Question. If an angle “x” possesses the attribute that it is a straight line and another angle “y” is made by a vertical line and horizontal line. The angles “x” and “y” are
(a) right angle and straight angle
(b) obtuse angle and acute angle
(c) straight angle and right angle
(d) straight angle and obtuse angle
Answer: (c) straight angle and right angle

Question. In the given figure \( \angle\text{BOE} \) represents

(a) An acute angle
(b) a right angle
(c) an obtuse angle
(d) a straight angle
Answer: (a) An acute angle

Question. How many lines are perpendicular to the line q in the given figure

(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2

Question. With respect to the figure given above, which of the following figure is an acute angle

(a) \( \angle\text{AOD} \)
(b) \( \angle\text{COD} \)
(c) \( \angle\text{AOB} \)
(d) \( \angle\text{BOD} \)
Answer: (a) \( \angle\text{AOD} \)

Question. Which of the following statements is incorrect with respect to the given figure?

(a) \( \text{PT} = \text{WZ} \)
(b) \( \text{QS} = \text{UW} = \text{XZ} \)
(c) \( \text{T} \) is the mid-point of \( \text{QW} \)
(d) \( \text{X} \) is the mid-point of \( \text{WZ} \)
Answer: (a) \( \text{PT} = \text{WZ} \)

Question. A three dimensional figure which has two bases of identical polygons which are separated by equal distances and whose lateral faces are rectangular in shape is a
(a) prism
(b) pyramid
(c) sphere
(d) cylinder
Answer: (a) prism

Choose the correct option:-

Q1 The angle formed between the east and the north direction is___________
a) 60°
b) 80°
c) 90°
d) 180°

Q2 A triangle can have _______ right angles.
a) One
b) Two
c) Three
d) None of these

Q3 If a bicycle wheel has 36 spokes , then the angle between a pair of adjacent spokes is
a) 10°
b) 15°
c) 12°
d) 20°

Q4 An angle more than 180° and less than 270° is called
a) Zero angle
b) Right angle
c) Reflex angle
d) Straight angle

Q5 What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
(a) 6 to 12
(b) 5 to 8

Q6 Which direction will you face if you start facing
(i) West and make 􀫚
􀫛 of a revolution clockwise?
(ii) East and make one full revolution?

Q7 What part of a revolution have you turned through if you stand facing
(i) North and turn clockwise to face west?
(ii) South and turn anticlockwise to face west?

Q8 Where will the hour hand of a clock stop if it starts:
(i) from 7 and turns through 1 right angle?
(ii) from 11 and turns through 3 right angles?

Q9 Fill in the blanks using appropriate signs (< , > or = )

(i) The measure of one complete angle……………… 360˚

(ii) The measure of reflex angle ………………… 180˚

(iii) The measure of an obtuse angle …………………90˚

(iv) The measure of an acute angle …………………..90˚

(v) The measure of right angle …………………….90˚

Q10 Write all the alphabets that are made of perpendicular lines.

Q11 Name the type of triangles:

(i) 6.5 cm, 8cm, 8.5 cm

(ii) 9 cm, 9 cm, 9 cm

(iii) 30˚, 60˚, 90˚

(iv) 99˚, 50˚, 31˚

(v) 46˚, 58˚, 76˚

(vi) ΔABC with ∠ B=90˚, AB = BC = 6cm

Q12 Fill in the blanks:

(i) The opposite sides of a rectangle are …………..

(ii) A rectangle whose adjacent sides are equal is called………………….

(iii) The opposite sides of a parallelogram are ………………… and …………………..

(iv) A …………….. is a rectangle with a pair of adjacent sides equal.

(v) One right angle = …………… of a revolution

Q13 Make the statement true using ‘All’ or ‘some’ or ‘no’

(i) …………….parallelograms are also quadrilaterals.

(ii) ………………….parallelograms are also trapeziums.

(iii) …………………..rhombuses are squares.

(iv) ………………….trapeziums are quadrilaterals.

(v) …………………..squares are rhombuses.

(vi) …………………trapeziums are isosceles.

(vii) ……………….equilateral triangles are isosceles.

Q14 Define a regular polygon.

Q15 Give two examples of each from your daily life: Cuboid, Cone, Cube, Cylinder, Sphere

Q16 Complete the following table:

S.No	Solid Figure	Vertices	Faces	Edges
1	Cuboid
2	Cone
3	Cube
4	Cylinder
5	Sphere
6	Triangular Pyramid
7	Square Pyramid
8	Triangular Prism