Can AAA be criteria for congruence of triangle.
Suraj goes to Dussehra fare.
He visited mirror stall and finds various convex and concave mirrors.
He finds that the images are similar with each angle.
But the shape is different in each mirror.
Similarly, we can understand that
$AAA$
criteria is not for congruence.
So, letâ€™s check for
$AAA$
criteria for the congruence of triangle.
Consider, two triangles,
$â–³PQR$
and
$â–³UVW$
.
If the relation between the angles is given as,
So, both the triangles are similar.
Here, the angles are equal but the triangles are totally different.
So, we get that
$AAA$
cannot be a criteria for congruence.
Letâ€™s see the proof of this criteria.
Consider a
$â–³ABC$
.
Now, draw
$ST$
parallel to
$BC$
.
So, the relationship between the angles is,
But, the shapes are different.
Both are similar to each other.
So,
$AAA$
cannot be a criteria for congruence.
Revision
The relationship between the angles is
$AAA$
.
But, the shapes are different, so
$AAA$
cannot be a criteria for congruence.
The End