Question

what else do you need to know to prove that they are congruent and which postulate are you using to prove their congruence?

Answer 1

The triangles PQR and FGH

We know that the corresponding angles

∠P=∠F

∠Q=∠G

> For the congruence postulate of Angle-Side-Angle to apply, the sides between them should be congruent to, that is:

$PQ=FG$

>For the congruence postulate of Angle-Angle-Angle to apply, the third angle of each triangle must be corresponding and congruent as well

$\angle R=\angle H$

> For the postulate Angle-Angle-Side to apply, two corresponding angle pairs must be congruent and two corresponding sides that are not between them must be congruent too, for example:

$QR=GH$

-or

$PR=FH$

>For the postulate Side-Side-Side to apply, all corresponding sides must be equal

$\begin{gathered} PQ=FG \\ QR=GH \\ PR=FH \end{gathered}$