8. Right angle-Hypotenuse-Side (RHS) congruence criterion

Right angled triangle:

 

From the examples given above, it is visible that the sides \(BC\), \(QR\), and \(YZ\) are the longest sides. These longest sides are the hypotenuses.

 

Hypotenuse:

The RHS congruence criterion is similar to the SAS congruence criterion.

 

The only difference is that \(90^\circ\) is the only angle used.

 

To prove that the two right angled triangles are congruent, it is enough to prove that any one side and the hypotenuse one triangle is congruent to the corresponding side and the hypotenuse of the other triangle.

 

 

From the figure given above, sides \(AB = PQ = 12\) \(cm\), and the hypotenuses \(BC = QR = 13\)\(cm\).

 

Since the corresponding sides and the hypotenuses are equal, the triangles \(\triangle ABC\) and \(\triangle PQR\) are congruent.