NCERT Textbook - Congruence of Triangles Class 7 Notes | EduRev

Mathematics (Maths) Class 7

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Class 7 : NCERT Textbook - Congruence of Triangles Class 7 Notes | EduRev

 Page 1


CONGRUENCE OF TRIANGLES 133 133 133 133 133
7.1  INTRODUCTION
Y ou are now ready to learn a very important geometrical idea, Congruence. In particular,
you will study a lot about congruence of triangles.
T o understand what congruence is, we turn to some activities.
Take two stamps (Fig 7.1) of same denomination. Place one stamp over
the other. What do you observe?
Fig 7.1
One stamp covers the other completely and exactly . This means that the two stamps are
of the same shape and same size. Such objects are said to be congruent. The two stamps
used by you are congruent to one another. Congruent objects are exact copies of one
another.
Can you, now, say if the following objects are congruent or not?
 1. Shaving blades of the same company [Fig 7.2 (i)].
 2. Sheets of the same letter-pad [Fig 7.2 (ii)]. 3. Biscuits in the same packet [Fig 7.2 (iii)].
4. T oys made of the same mould. [Fig 7.2(iv)]
(i) (ii) (iii) (iv)
Chapter  7
Congruence of
Triangles
DO THIS
Fig 7.2
Page 2


CONGRUENCE OF TRIANGLES 133 133 133 133 133
7.1  INTRODUCTION
Y ou are now ready to learn a very important geometrical idea, Congruence. In particular,
you will study a lot about congruence of triangles.
T o understand what congruence is, we turn to some activities.
Take two stamps (Fig 7.1) of same denomination. Place one stamp over
the other. What do you observe?
Fig 7.1
One stamp covers the other completely and exactly . This means that the two stamps are
of the same shape and same size. Such objects are said to be congruent. The two stamps
used by you are congruent to one another. Congruent objects are exact copies of one
another.
Can you, now, say if the following objects are congruent or not?
 1. Shaving blades of the same company [Fig 7.2 (i)].
 2. Sheets of the same letter-pad [Fig 7.2 (ii)]. 3. Biscuits in the same packet [Fig 7.2 (iii)].
4. T oys made of the same mould. [Fig 7.2(iv)]
(i) (ii) (iii) (iv)
Chapter  7
Congruence of
Triangles
DO THIS
Fig 7.2
MATHEMATICS 134 134 134 134 134
The relation of two objects being congruent is called congruence. For the present,
we will deal with plane figures only , although congruence is a general idea applicable to
three-dimensional shapes also. W e will try to learn a precise meaning of the congruence
of plane figures already known.
7.2  CONGRUENCE OF PLANE FIGURES
Look at the two figures given here (Fig 7.3). Are they congruent?
(i) (ii)
Fig 7.3
Y ou can use the method of superposition. T ake a trace-copy of one of them and place
it over the other . If the figures cover each other completely , they are congruent. Alternatively ,
you may cut out one of them and place it over the other. Beware! Y ou are not allowed to
bend, twist or stretch the figure that is cut out (or traced out).
In Fig 7.3, if figure F
1
 is congruent to figure F
2 
, we write F
1
 ? F
2
.
7.3  CONGRUENCE AMONG LINE SEGMENTS
When are two line segments congruent?  Observe the two pairs of line segments given
here (Fig 7.4).
       (i) (ii)
Fig 7.4
Use the ‘trace-copy’ superposition method for the pair of line segments in [Fig 7.4(i)].
Copy CD and place it on AB . Y ou find that CD covers AB , with C on A and D on B.
Hence, the line segments are congruent.   W e write AB CD ? .
Repeat this activity for the pair of line segments in [Fig 7.4(ii)]. What do you find?
They are not congruent.  How do you know it?  It is because the line segments do not
coincide when placed one over other.
Y ou should have by now noticed that the pair of line segments in [Fig 7.4(i)] matched
with each other because they had same length; and this was not the case in [Fig 7.4(ii)].
If two line segments have the same (i.e., equal) length, they are congruent.  Also,
if two line segments are congruent, they have the same length.
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