Question

PQR and PSR are two right triangles with hypotenuse PR. Prove that ∠PQS=∠PRS. ​

Answer 1

Answer:

In triangles PQS and PQR

∠P is common to both.

and ∠PSQ=∠PQR

Triangles PQS and PQR are equiangular

∴PQPS=QRQS

or, PS=QRPQ⋅QS ...(i)

Again, triangles QRS and PQR are equiangular

∴QRSR=PQQS

or, SR=PQQS⋅QR ...(ii)

From eqns. (i) and (ii)

SRPS=QRPQ⋅QS⋅QR⋅QSPQ=QR2PQ2