Question

In Fig $7.32$, measure of some parts of triangles are given. By applying $RHS$ congruence rule, state which pairs of triangles are congruent. In case of congruent triangles, write the result in symbolic form.

Answer 1

Given,

to find out wether the given figures are

Congruent using $RHS$

$\left(i\right)$ Congruence rule

so, Now let us consider figure $\left(i\right)$

as per $RHS$ congruence rule.

$LQ=LF={90}^o$ ($\because$ given)

$PR=FD$ (given)

$PQ\ne DE$ ($\because$ given in figure $\left(i\right)$)

$\therefore △PQR$ is not congruence to $△DEF$

$\left(ii\right)$ Now let us consider figure $\left(i\right)$

as per $RHS$ congruence rule

$LC=LD={90}^o$ ($\because$ given )

$AC=BD$ ($\because$ given)

$AB=AB$ ($\because$ common side)

$\therefore △ABC\cong △ABD$

$\left(iii\right)$ Now let us consider figure $\left(iii\right)$

as per $RHS$ congruence rule we get,

$\angle B=\angle D={90}^o$ ($\because$ given)

$AB=AD$ ($\because$ given)

$BC=CD$ ($\because$ given)

$\therefore △ABC\cong △ADC$

$\left(iv\right)$ Let us consider figure $\left(iv\right)$

as per $RHS$ congurence rule we get,

$\angle S=\angle S={90}^o$ (common angle )

$PQ=PR$ ($\because$ given)

$QS=SR$ ($\because$ common base)

$\therefore △PSQ\cong △PSR$