Question

Given : $RS$ and $PT$ are altitudes of $\Delta PQR$. Prove that :

i) $\Delta PQT$ ∼ $\Delta RQS$

Answer 1

Step $1$ : Drawing the figure

Given : $RS$ and $PT$ are altitudes of $\Delta PQR$.


Step $2$ : Proving $\Delta PQT$ ∼ $\Delta QRS$

Now, in $\Delta PQT$ and $\Delta RQS$,
$\angle PQT=\angle RQS$ [Common angle]
And $\angle PTQ=\angle RQS$
[ Both are ${90}^{\circ },\because RS$ and $PT$ are altitudes ]
So, $\Delta PQT$ ∼ $\Delta RQS$ by $AA$ criterion.
Hence proved.