Congruence of Triangles
Suresh went to a barber shop for hair cut with his elder brother.
There he observed his image in the mirror hanging on the wall.
He noticed that his image have the same shape and size as his body.
This made him curious, as he took a triangular hanger lying beside him also shown the same image in the mirror
And again he observed that the image of triangular hanger is same as the original hanger.
While going back from the shop, Suresh told his brother about his observation.
He said that the images that objects cast in the mirror have similar shape and size as the objects themselves.
Further he explained that, those objects which have same shape and size are known as congruent objects.
Similarly, the image of the triangular hanger is congruent to the hanger or they are congruent triangles.
Let’s try to help Suresh to understand the term “Congruent triangles”.
Suppose we have two triangles
$△ABC$
and
$△PQR$
with sides as shown
Now, in
$△ABC$
and
$△PQR$
, the sides
And, when we place either of the triangles on another, it covers the second triangle completely.
So, we get that
$∠BAC=∠QPR$
,
$∠ABC=∠PQR$
and
$∠ACB=∠QRP$
.
So, the two triangles have all the corresponding sides and angles equal, therefore they are congruent.
So, if the corresponding sides of two triangles are equal, the triangles are known as congruent.
But only the equality of the corresponding angles in two triangles does not make them congruent.
Suppose we have two triangles,
$△ABC$
and
$△MNO$
. As
And, these two triangles have all the corresponding angles equal, but the lengths of the sides are different
But, when we place either of the triangles on another, it does not cover the second triangle completely.
Hence, these two triangles are not congruent, even when the measures of corresponding angles are same.
Revision
Two triangles are said to be congruent if their shapes and size are same (superpose each other).
If two triangles have same sides and angles then they are congruent irrespective of their orientation.
The End