Download Remedial - MoreMaths

1. Revision
Description
Recall basics of
geometrical shapes.
Reflect and Review
A book, a birthday cap and a
dice are some examples of 3-D
shapes.
Teasers
1) Write two examples of 2-D
shapes and 3-D shapes from
your day-to-day life.
2. Comparing the Lengths of Line Segments
Description
Reflect
and
Review
 The lengths of line segments can be compared See
by observation. But this method is not
below
applicable in all situations.
the
 Comparing can also be done by tracing, i.e.,
table
we take a tracing paper and make the replica


of one line segment and keep this traced sheet
on the second line segment and then find out
which is longer. But this is time consuming.
Comparing lengths of line segments can be
done by using ruler. We place one end of the
first line segment at 0 mark of the ruler and
find the position where the other end of the
segment is with respect to the ruler. Similarly
we find the length of other line segments and
compare.
The best way of comparing the lengths of two
line segments is using a divider.
We open the divider in such a way that the
two tips of the divider coincide with the two
ends of a line segment. Now without
disturbing the opening of the divider, we place
it in such a way that the tip of one of its arm
coincides with one end of second segment and
then check whether the tip of the other arm
coincides with the other end or not.
Teasers
See
below
the
table
Answers
1) Length of
̅̅̅̅
< Length of
̅̅̅̅
< Length of
̅̅̅̅.
1
Reflect and Review:
B
l
D
A
C
Here, line segmentl AB is smaller than segment CD on observation.
Teasers:
1) Compare the lengths of the line segments PQ, QR and RS from the below figure.
m
P
Q
S
R
3. Collinear and Non-collinear Points
Description
Reflect and
Teasers
Review
See below the
See below the See below the
table
table
table
Answers
1) Y is the midpoint of
̅̅̅̅ .
Description:
If three or more points are lying on the same line then they are called collinear points and the
points which do not lie on the same line are called non-collinear points.
Reflect and Review:
l
A
B
C
D
Here, points A, B, C and D are collinear.
Teasers:
1) Find which points in the following figure are mid-points of the other two.
t
X
l
2
Y
Z
W
4. Parallel and Perpendicular lines; Concurrent lines
Description
Reflect and Review
The
altitudes
of a triangle are concurrent,
See below the
since they intersect at the orthocentre.
table
Teasers
1) Give some examples of
concurrent lies that you
know.
Description:

If two lines m and n never intersect each other and the distance between them is the same
always, then they are said to be parallel to each other, and it is represented as m  n.
m
n

If two lines m and n intersect each other at a point O making a right angle, then they are said
to be perpendicular to each other, and it is represented as m ⊥ n.
m
O
n

If three or more lines pass through the same point, then they are called concurrent lines.
l
q
m
p
n
3
5. Angles – Right, Straight and Complete
Description Reflect and Review
If the hour’s hand of a
See below
clock turns (clockwise)
the table
from 2 to 5, it moves one
right angle.
Teasers
1) Where will the hand of a
clock stop, if it starts at 4
and makes of a
revolution?
Answers
1) At 12
o’clock
2) South
2) Which direction will you
face if you are initially facing
East and then make ¼ of a
revolution clockwise?
Description:
1) Taking a left turn (Anti-clockwise) or right turn (Clockwise) from the present position is said
to be turning about right angle.
2) Turning two right angles in the same direction is said to be making a straight angle.
3) Turning four right angles in the same direction or turning two straight angles in the same
direction makes a full turn. One complete turn is called one revolution. The angle turned to
make one revolution is called a complete angle.
4) When the hand of a clock turns from one point and returns to the same position, it
completes one revolution.
N
W
Anti-clock
wise
E
Right Angle i.e.,
one right turn
Straight angle i.e., two right turns
S
Clock wise
Three right turns
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6. Angles – Acute, Obtuse, Reflex
Description
Reflect and
Review
Angle measuring 1790
See below
is said to be an obtuse
the table
angle, since it is more
than 900 and less than
1800.
Teasers
1) Pick out the acute,
obtuse, reflex, right,
straight and
complete angles
from the following:
900, 890, 1800, 3600,
2610, 1120, 680,
3450, 1370, 2700
Answers
1) Acute angles:
890 and 680
Right angles:
900
Obtuse angles:
1120, 1370
Straight angles:
1800
Reflex angles:
2610, 2700, 3450
Complete angles:
3600
Description:



An angle whose measure is less than a right angle is called an acute angle.
An angle whose measure is more than a right angle but less than a straight angle is called an
obtuse angle.
A reflex angle is larger than a straight angle.
Measuring angles:
 To measure an angle we need a tool or an instrument called Protractor.
 It is divided into 180 equal parts, each part measures one degree denoted as 1°.
 The marking starts from 0° on the right side and ends with 180° on the left side and vice
versa.
 To measure an angle using a Protractor
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1) Place the protractor in such a way that the midpoint of the straight edge of the protractor
coincides with point B.
2) Adjust the position of the protractor so that the straight edge coincides with the arm BC of
angle ∠ABC.
3) There are two scales on the protractor. We should consider the scale whose ‘0’-mark
coincides with the horizontal straight edge.
4) The mark shown by AB on the curved edge gives the measure of the angles. Here it is 60°.
So, ∠ABC = 60°.
7. Triangles
Description
See below the
table
Reflect and Review
Teasers
Answers
1) Rightangled
and
isosceles
triangle

A triangle with sides 5 cm,
5 cm and 6 cm is said to be
an isosceles triangle, since
it has two of its sides equal.
1) Name the
triangle with
angles 450,
450, 900.

A triangle with angles 350,
550 and 900 is said to be a
right angled triangle, since
one of its angles is 900.
2) Can any
triangle have
one right
angle and one
obtuse angle?
Description:


6
A polygon which has three sides is called a triangle.
Types of triangles based on sides
 A triangle having all three sides unequal is called a scalene triangle.
 A triangle having two equal sides is called an isosceles triangle.
 A triangle having all three sides equal is called an equilateral triangle.
2) No.

Types of triangles based on angles
 If all the angles of a triangle are less than 900, then it is called an acute-angled triangle.
 If one angle of a triangle is a right angle, then it is called a right-angled triangle.
 If one angle of a triangle is obtuse, then it is called an obtuse-angled triangle.
8. Quadrilaterals
Description
Reflect and Review
See below
A square is said to be a
regular polygon, since
the table
0
each of its angle is 90 and
all sides are equal.
Teasers
Answers
1) Name the quadrilateral
which satisfies the
properties of both
rectangle and rhombus.
1) Square
2) Isosceles
trapezium
2) Name a trapezium whose
non-parallel sides are
equal.
Description:



A four-sided polygon is called a quadrilateral. It has four sides, four angles and two diagonals.
There are different types of quadrilaterals and special quadrilaterals have different properties
based on their sides, angles and diagonals.
A quadrilateral in which
 One pair of opposite sides are parallel is called a trapezium.
 Both the pairs of opposite sides are parallel is called a parallelogram.
 All the sides are equal is called a rhombus
 Both the pairs of opposite sides are parallel and each angle is 900 is called a rectangle.
 All sides are equal and each angle is 900 is called a square.
 In which two pairs of adjacent sides are equal is called a kite.
Parallelogram
Rhombus
Trapezium
Rectangle
Kite
Square
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9. Polygons
Description
See below
the table
Reflect and
Review
Teasers
A polygon which has no Name the polygons given below.
diagonal is a triangle,
1)
since no vertex of a
triangle have an
opposite vertex, it has
only an opposite side.
Answers
1) Irregular
hexagon
2) Irregular
decagon
2)
Description:


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A closed rectilinear figure with three or more sides is called a polygon.
A polygon in which all the sides are equal and all the angles are equal is called a regular
polygon.
10.Three-dimensional (3-D) Shapes
Description Reflect and Review
A prism with circle bases
See below
is called a cylinder. Since,
the table
all its other faces become
one curved surface.
Teasers
Answers
1) Name a three-dimensional
shape that has no vertices
and edges.
2) Name the prism in which the
base of a prism is a circle and
its surrounding triangular
faces are all curved as one
face.
1) Cylinder
2) Cone.
Description:





Shapes having length, breadth and height are called three-dimensional shapes.
Cuboid, cube, prism, pyramid, cylinder, cone, sphere are some of the three-dimension shapes
that we come across in our day-today life.
The flat surfaces are called the faces of a solid shape.
Two faces meet at a line segment. This line segment is called an edge of the solid.
Three edges meet at a point. The point of intersection of the edges is called the vertex of the
solid.
A prism has two identical bases and all its other faces are rectangles.
A pyramid has triangular surfaces around and bases are different polygons.
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Cuboid
Cube
Cylinder
Cone
Sphere
Prism
Pyramid
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