QUESTION

# It is to be established by the RHS congruence rule that $\Delta ABC=\Delta RPQ$. What additional information is needed, if it is given that $\angle B=\angle P={{90}^{\circ }}$ and AB = RP?

Hint: Draw both triangles ABC and RPQ. State the RHS congruence and compare both the triangle with respect to the theorem and find out the additional information.

RHS Congruence Rule states that in two right – angled triangles, if the length of the hypotenuse and one side of one triangle is equal to the length of the hypotenuse and one side of the other triangle, then the two triangles are congruent.

Thus the additional information needed is the length of hypotenuse.

So for $\Delta ABC$ and $\Delta RPQ$ to be congruent the hypotenuse of both these triangles should be the same. So we can say that,
AC = RQ

Thus by RHS congruence $\Delta ABC$ is equal to $\Delta RPQ$, when $\angle B=\angle P={{90}^{\circ }}$.
AB = RP and AC = RQ

Thus we got the additional information as AC = RQ.

Note: Apart from RHS congruence, there is SSS congruence. If in 2 triangles, the three sides of one triangle is equal to the three sides (SSS) of another triangle then the 2 triangles are congruent.