In the shown diagram, prove the similarity of
\(
△PQS\) and
\(△TQR\), given that
\(\frac{QR}{QS} = \frac{QT}{PR}\)
and
\(\angle 1 = \angle 2\).
Proof:
Given \(\angle 1 = \angle 2\)
Side opposite to equal angles are equal.
\(PR =\) - - - - (1)
Also, given \(\frac{QR}{QS} = \frac{QT}{PR}\)
\(\frac{QR}{QS} =\) - - - - (2)
In \(\Delta PQS\) and \(\Delta TQR\),
\(\angle PQS =\) ()
\(\frac{QR}{QS} = \frac{QT}{QP}\)
\(\Delta PQS \sim \Delta TQR\) (by )
Hence proved.