Question

In the figure, seg $PS$ intersects seg $TK$ in the point $R$. $\angle T$ and $\angle K$ are right angles. State whether $△PTR$ and $△SKR$ are similar. If yes, by which test?

Answer 1

Given: $\angle PTR=\angle SKR={90}^o$

To prove : $△PTR\sim △SKR$

In $△PTR$ and $△SKR$

$\angle PTR=\angle SKR={90}^o$ [Given]

$\angle PTR=\angle SRk$ [Vertically opposite angles]

$△PTR\sim △SKR$ [by similarity rule]

Hence prove