RHS Criteria of congruence of triangles

Suppose, you have taken a rectangular sheet in your hands.

You cut it along its diagonal.

Thus, this rectangular sheet is divided in two triangles.

Here, it is important to know that any such two triangles would always be congruent to each other.

This can be proved practically by superposition.

Or we can use other method of RHS criterion to prove this congruency.

Let’s understand the RHS criterion for triangles.

Suppose two triangles are given as

is perpendicular to and is perpendicular to , so both triangles are right angled triangles

Suppose we are given , and i.e.

criteria specifies right angle, hypotenuse and side

RHS congruence criterion specifies that if hypotenuse and one side of two right angled triangles are equal, then both triangles are congruent.

By congruence rule both the triangles are congruent

Let’s understand RHS congruence rule with another example.

Suppose we are given with figure as such and AC = BD

= = in and .

Hypotenuse of both triangles are equal and side is common in both triangle

So both the triangles & are congruent by congruence.

Revision

RHS criteria for congruence specifies that hypotenuse and one side of two right angle triangles are equal, both triangles are congruent.

The End