Congruence of Line Segments
A boy is sitting on the bridge over a canal at
$12:00$
pm.
The sun is shining right above him i.e. in the center of the sky.
He sees a stick floating on the surface of the stable water.
Since, the sun is shining exactly in center of the sky
As a result, the length of the stick is exactly the same as its reflection in the bottom of pond.
And, reflection can’t be seen from the upper side.
But, as the sun moves, the length of reflection increases and he is able to see the reflection.
We can understand this whole incident from the point of view of mathematics.
Let’s understand it through mathematics.
Since, the sun shines exactly in the center of sky
So, the stick and it’s reflection, both fall along the same line and the length of reflection is same as length of stick.
You can try this experiment in real life and verify it.
Now, if we place the stick on it’s reflection, we get that both cover each other completely.
This is known as superposition.
If we consider the stick as a line segment
$AB$
.
and, the reflection as line segment
$CD$
.
In this way, we place the point
$A$
on
$C$
&
$B$
on
$D$
.
We see that both cover each other. So, we say both line segments are congruent to each other.
Thus, we conclude that if two lines have same lengths, both are called congruent to each other.
Also, if two lines are congruent to each other, both of them have same length.
In the same way, we can check the congruence of angles.
Let’s check the congruence of angles.
We have two angles as
First, we place
$A$
on
$P$
and then
$AB$
on
$PQ$
.
Since, both have same measures, so
$∠PQR$
matches
$∠ABC$
exactly.
Therefore, both angles are said to be congruent to each other.
Also, if two angles are congruent to each other, both have same measures.
Revision
Two line segments are said to be congruent to each other, if both have same lengths.
Two angles are said to be congruent to each other, if both have same measures.
The End