Prove that the angles opposite to equal sides of a triangle are equal.

Here, △PQR ,PR=QR

Now we draw perpendicular from R to PQ which cuts PQ at T.

Now,

In △PRT and △QRT,

∠PTR=∠QTR=90^o

RT is the common side

PR=QR , [Hypotenuses]

Therefore, △PRT≃△QRT [By Rightangle-Side-Hypotenuse (RHS) property of congruence]

∠RPT=∠RQT [CPCT]

Hence the angles opposite to PR,QR are also equal, proved.

Hence it is proved that the angles opposite to equal sides of a triangle are equal.