QUESTION BANK CLASS 6 UNDERSTANDING ELEMENTARY SHAPES
- What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 3 to 9
a) 1/2 b) 3/4 c) 2/3 d) 1/4
- What is the measure of straight angle?
a) 75° b) 0° c) 90° d) 180°
- Name the types of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b)ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) PQR such that PQ = QR = PR = 5cm
- Name the types of following triangles:
- (a) D LMN with mÐ L = 30° , mÐ M = 70° and mÐ N = 80° .
(b)DABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) D DEF with mÐ D = 90°
Identify open curve.
Measure and classify each angle:
- What is the measure of right angle?
a) 75° b) 0° c) 90° d) 180°
- How many lines can pass through one given point?
a) 0 b) 1 c) 2 d) infinitely
- Where will the hand of a clock stop if it starts at 12 and make 1/2 of a revolution, clockwise?
- Where will the hour hand of a clock stop if it starts from 6 and turns through 1 right angle?
- Which direction will you face if you start facing East and make 11/2 of a revolution clockwise?
- What part of a revolution have you turned through if you stand facing East and turn clockwise to face North?
- Which direction will you face if you start facing East and make 11/2 of a revolution clockwise?
EXTRA TRY THESE QUESTIONS
1. A cuboid looks like a rectangular box.
It has 6 faces.
Each face has 4 edges.
Each face has 4 corners (called vertices).
2. A cube is a cuboid whose edges are all of equal length.
It has ______ faces.
Each face has ______ edges.
Each face has ______ vertices.
3. A triangular pyramid has a triangle as its base.
It is also known as a
tetrahedron.
Faces : _______
Edges : _______
Corners : _______
4. A square pyramid has a square as its base.
Faces : _______
Edges : _______
Corners : _______
5. A triangular prism looks like the shape of a Kaleidoscope.
It has triangles
as its bases.
Faces : _______
Edges : _______
Corners : _______
EXERCISE 5.1
1. What is the disadvantage in comparing line
segments by mere observation?
2. Why is it better to use a divider than a ruler, while measuring the length of a line
segment?
3. Draw any line segment, say AB. Take any point C lying in between A and B.
Measure the lengths of AB, BC and AC.
Is AB = AC + CB?
[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we
can be sure that C lies between A and B.]
4. If A,B,C are three points on a line such that AB = 5 cm, BC = 3 cm and
AC = 8 cm, which one of them lies between the other two?
5. Verify, whether D is the mid point of AG .
6. If B is the mid point of AC and C is the mid
point of BD, where A,B,C,D lie on a straight line, say why AB = CD?
7. Draw five triangles and measure their sides. Check in each case, if the sum of
the lengths of any two sides is always less than the third side
EXERCISE 5.2
1. What fraction of a clockwise revolution does the hour hand of a clock turn through,
when it goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
2. Where will the hand of a clock stop if it
(a) starts at 12 and makes
1/2 of a revolution, clockwise?
(b) starts at 2 and makes
1/2 of a revolution, clockwise?
(c) starts at 5 and makes
1/4 of a revolution, clockwise?
(d) starts at 5 and makes
3/4 of a revolution, clockwise?
3. Which direction will you face if you start facing
(a) east and make
1/2 of a revolution clockwise?
(b) east and make 1
1/2 of a revolution clockwise?
(c) west and make
3/4 of a revolution anti-clockwise?
(d) south and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why not?)
4. What part of a revolution have you turned through if you stand facing
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
5. Find the number of right angles turned through by the hour hand of a clock when
it goes from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6
6. How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
(c) west and turn to west?
(d) south and turn to north?
7. Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
EXERCISE 5.3
1. Match the following :
(i) Straight angle - (a) Less than one-fourth of a revolution
(ii) Right angle - (b) More than half a revolution
(iii) Acute angle - (c) Half of a revolution
(iv) Obtuse angle - (d) One-fourth of a revolution
(v) Reflex angle - (e) Between
1/4 and
1/2 of a revolution
- (f) One complete revolution
2. Classify each one of the following angles as right, straight, acute, obtuse or reflex :
EXERCISE 5.4
1. What is the measure of (i) a right angle? (ii) a straight angle?
2. Say True or False :
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle < 90°.
(c) The measure of a reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m ∠A = 53° and m ∠B = 35°, then m ∠A > m ∠B .
3. Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
4. Measure the angles given below using the Protractor and write down the measure
5. Which angle has a large measure?
First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
6. From these two angles which has
larger measure?
Estimate and then
confirm by measuring them.
7. Fill in the blanks with acute, obtuse,
right or straight :
(a) An angle whose measure is less
than that of a right angle is______.
(b) An angle whose measure is greater than that of a right angle is ______.
(c) An angle whose measure is the sum of the measures of two right angles
is _____.
(d) When the sum of the measures of two angles is that of a right angle, then
each one of them is ______.
(e) When the sum of the measures of two angles is that of a straight angle and if
one of them is acute then the other should be _______.
8. Find the measure of the angle shown in each figure. (First estimate with your
eyes and then find the actual measure with a protractor).
9. Find the angle measure between the hands of the clock in each figure :
In the given figure, the angle measures 30°.
Look
at the same figure through a magnifying glass.
Does the angle becomes larger?
Does the size
of the angle change?
11. Measure and classify each angle :
EXERCISE 5.5
1. Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter V.
2. Let PQ be the perpendicular to the line segment XY .
Let PQ and XY intersect
in the point A.
What is the measure of ∠PAY ?
3. There are two set-squares in your box.
What are the measures of the angles that
are formed at their corners?
Do they have any angle measure that is common?
4. Study the diagram. The line l is perpendicular to line m
(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EH.
EXERCISE 5.6
1. Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ∆PQR such that PQ = QR = PR = 5 cm.
(d) ∆DEF with m ∠D = 90°
(e) ∆XYZ with m ∠Y = 90° and XY = YZ.
(f) ∆LMN with m ∠L = 30°, m ∠M = 70° and m ∠N = 80°.
2. Match the following :
Measures of Triangle - Type of Triangle
(i) 3 sides of equal length - (a) Scalene
(ii) 2 sides of equal length - (b) Isosceles right angled
(iii) All sides are of different length - (c) Obtuse angled
(iv) 3 acute angles - (d) Right angled
(v) 1 right angle - (e) Equilateral
(vi) 1 obtuse angle - (f) Acute angled
(vii) 1 right angle with two sides of equal length - (g) Isosceles
3. Name each of the following triangles in two different ways:
(you may judge the
nature of the angle by observation).
4. Try to construct triangles using
match sticks.
Some are shown here.
Can you make a triangle with
(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 matchsticks?
(d) 6 matchsticks?
(Remember you have to use all the
available matchsticks in each case)
Name the type of triangle in each case.
If you cannot make a triangle, think of reasons for it.
EXERCISE 5.7
1. Say True or False :
(a) Each angle of a rectangle is a right angle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.
2. Give reasons for the following :
(a) A square can be thought of as a special rectangle.
(b) A rectangle can be thought of as a special parallelogram.
(c) A square can be thought of as a special rhombus.
(d) Squares, rectangles, parallelograms are all quadrilaterals.
(e) Square is also a parallelogram.
3. A figure is said to be regular if its sides are equal in length and angles are equal
in measure.
Can you identify the regular quadrilateral?
EXERCISE 5.8
1. Examine whether the following are polygons. If any one among them is not, say
why?
2. Name each polygon.
Make two more examples of each of these.
3. Draw a rough sketch of a regular hexagon.
Connecting any three of its vertices, draw
a triangle.
Identify the type of the triangle you have drawn.
4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish).
Draw a
rectangle by joining exactly four of the vertices of the octagon.
5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side
of the polygon. Draw a rough sketch of a pentagon and draw its diagonals
EXERCISE 5.9
1. Match the following :
(a) Cone (i)
(b) Sphere (ii)
(c) Cylinder (iii)
(d) Cuboid (iv)
(e) Pyramid (v)
Give two new examples of each shape.
2. What shape is
(a) Your instrument box?
(b) A brick?
(c) A match box?
(d) A road-roller?
(e) A sweet laddu?
POINTS TO REMEMBER
1. The distance between the end points of a line segment is its length.
2. A graduated ruler and the divider are useful to compare lengths of line
segments.
3. When a hand of a clock moves from one position to another position we have
an example for an angle.
One full turn of the hand is 1 revolution.
A right angle is ¼ revolution and a straight angle is ½ a revolution .
We use a protractor to measure the size of an angle in degrees.
The measure of a right angle is 90° and hence that of a straight angle is 180°.
An angle is acute if its measure is smaller than that of a right angle and is obtuse
if its measure is greater than that of a right angle and less than a straight angle.
A reflex angle is larger than a straight angle.
4. Two intersecting lines are perpendicular if the angle between them is 90°.
5. The perpendicular bisector of a line segment is a perpendicular to the line
segment that divides it into two equal parts.
6. Triangles can be classified as follows based on their angles:
Nature of angles in the triangle Name
Each angle is acute Acute angled triangle
One angle is a right angle Right angled triangle
One angle is obtuse Obtuse angled triangle
7. Triangles can be classified as follows based on the lengths of their sides:
Nature of sides in the triangle Name
All the three sides are of unequal length Scalene triangle
Any two of the sides are of equal length Isosceles triangle
All the three sides are of equal length Equilateral triangle
8. Polygons are named based on their sides.
Number of sides Name of the Polygon
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
8 Octagon
9. Quadrilaterals are further classified with reference to their properties.
Properties Name of the Quadrilateral
One pair of parallel sides Trapezium
Two pairs of parallel sides Parallelogram
Parallelogram with 4 right angles Rectangle
Parallelogram with 4 sides of equal length Rhombus
A rhombus with 4 right angles Square
10. We see around us many three dimensional shapes.
Cubes, cuboids, spheres,
cylinders, cones, prisms and pyramids are some of them
