Question

You want to show that $\Delta ART\cong \Delta PEN$, and you are to use $ASA,SAS,SSS$ criterion, you need to have which conditions?

Answer 1

Consider the diagram shown below.

If $\Delta ART\cong \Delta PEN$,

For $ASA$ criteria, two angles and the side between them must be equal.

Therefore,

$AT=PN$ (given)

So,

$\angle A=\angle P$

$\angle T=\angle N$

For $SAS$ criteria, two sides and the sideangle between them must be equal.

Therefore,

$\angle T=\angle M$ (given)

So,

$RT=EN$

$PN=AT$

For $SSS$ criteria, all three sides must be equal.

Therefore,

$AR=PE$

$RT=EN$

$AT=PN$

Hence, using these conditions we can show that $\Delta ART\cong \Delta PEN$.