Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why triangle hij is congruent to triangle klm

  AAS since you have two angles and one side. 

LA (never heard of it but if it's actually a theorem then yes. It makes sense in right triangles) 

LL (same as LA) 

HL since the hypotenuse and the leg are congruent. 

SAS CAN be used BUT only if you're going to prove that the sides CE and OQ are congruent or the angles D and P are congruent. You cannot directly apply this. 

ASA CAN be used BUT, as with SAS, can only be used if you prove that either the sides CE and OQ are congruent or the angles D and P are congruent. You cannot directly apply this