If $\angle E=\angle S$ and $G$ is the midpoint of $ES$, Prove that $△GET\equiv △GST$

If $\angle YTB\equiv \angle YBT$ and $\angle BOY\equiv \angle TRY$, prove that $∆BOY\equiv ∆TRY$

If TAP is an isosceles triangle with $TA = TP$ and $\angle TSA=90°$.

Is $∆TAS\equiv ∆TPS$?

If TAP is an isosceles triangle with $TA = TP$ and $\angle TSA=90°$.

Is $\angle P\equiv \angle A$?

If TAP is an isosceles triangle with $TA = TP$ and $\angle TSA=90°$.

Is $AS=PS$?

In the below given figure, if $∆PQR~∆XYZ$, find $a$ and $b$.

In the below given figure, $\angle ABC\equiv \angle EDC$ and the perimeter of $∆CDE$ is $27$ units, prove that $AB\equiv EC$.

In the below given figure, if $\angle 1\equiv \angle 3$ and $\angle 2\equiv \angle 4$ then, prove that $∆BIG~∆FAT$. Also find $FA$.

If $A$ is the midpoint of $RU$ and $T$ is the midpoint of $RN$, prove that $∆RAT~∆RUN$.