Important Questions: Understanding Elementary Shapes | Mathematics (Maths) Class 6 PDF Download

Q1: All equilateral triangle are isosceles, but all isosceles triangle are not equilateral. Justify the statement.
Ans: An isosceles triangle is any triangle with 2 sides that are equal in length. So every equilateral triangle is a special case of an isosceles triangle since not just 2 sides are equal, but all 3 are. But every isosceles triangle is not equilateral, because you can have 2 sides of equal length and a third side that is either longer or shorter than those 2 sides. For example, if the triangle is a right-angle triangle and the two sides that meet to make the right angle are the same length, then the 3rd side would be longer than those two.

Q2: Draw a rough sketch of a regular octagon. Draw a rectangle by joining exactly four of the vertices of the octagon.
Ans:

Q3: Draw a hexagon and write its sides and diagonals?
Ans: Hexagon

Sides of hexagon: AB, BC, CD, DE, EF and FA.
Diagonals of hexagon: AC, AD, AE, BD, BE, BF, CE, CF, and DF

Q4: How many faces a tetrahedron have?
Ans: In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex.

Q5: Fill up the following:
(a) Measure of a complete angle is ____________^o.
(b) The triangle in which ____________ sides are equal is called isosceles triangle.
(c) Each of its angles rectangle measures ____________^o.
(d) A cube has ____________ vertices.
Ans: (a) 360
(b) two
(c) 90
(d) 8

Q6: How do we write  symbolically?
Ans: 

Q7: What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 12 to 3?
Ans: In clock hour hand moves 12 hr from 12 o’ clock to 12 o’ clock. Fro12 to it 3 it is 3 hr, so fraction of 3 hr from 12 hr = 3/12 = 1/4. Or, the hour hand moves 360^o form 12 to 12, from 12 to 3 it moves 90^o, so fraction of 90o from 360^o = 90/360 = 1/4.

Q8: How many right angles do you make if you start facing south and turn clockwise to west?
Ans: The four main direction north, east, south, west. Each of them are at 90^o clockwise, i.e. we have to move 90^o to move north to east, another 90^o from east to south like that. So South to west we have to move only one 90^o. So answer is 1.

Q9: Measure the angles given below, using the Protractor and write down the measure.

Ans: (a) 45°
(b) 125°
(c) 90°
(d) ∠1 = 40°, ∠2 = 125° and ∠3 = 95°.

Q10: If B is the mid point ofwhere A, B, C, D lie on a straight line, say why AB = CD?
Ans:

In view of (1) and (2), we get
AB = CD.

Q11: What is the angle name for half a revolution?
Ans: Straight Angle (180°)

Q12: State true or false:
(a) Sum of any two sides of a triangle is greater than the third side.
(b) An equilateral triangle is also considered as an isosceles triangle
(c) A polygon is regular if its all sides are equal.
(d) Opposite faces of a cuboid are equal in size.
Ans: (a) True
(b) False; in isosceles triangle only two sides are equal.
(c) False; For a polygon to be regular, all sides as well as all angles have to be equal.
(d) True

Q13: Match the following 3D shape and its edges.
Ans:

Q14: What is the angle name for half a revolution?
Ans: One revolution = 360^o
Half revolution
180^o is called straight angle

Q15: Find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 6.
Ans: Hour hand move 360^o from 12 to 12. So it moves 3 hr from 3 to 6. The factor of 3 to 12 = 3/12 = 1/4
Right angle = 90^o , factor of 90^o with 360^o = 90/360 = 1/4.
So Hour hand will turn one right angle to cross 3 to 6.