Based only on the information given in the diagram, which congruence theorems and postulate could be given as reasons why ABC = DEF? Multiple choice.

Now I know the answer is not B & C and the answer for sure is A & D, but should I also put E & F? I'm hesitating because the first four are RIGHT triangle congruence theorems while the last two are OTHER triangle congruence theorems/postulates. I'm not sure if we are "allowed" to use the right angle as a way to prove congruence.
Does that make sense??

A) LL
B) HA
C) HL
D) LA
E) AAS
F) SAS

This is useful here because LL stands for Leg Leg. It says that if we know that a pair of leg lengths of two right triangles are the same, then overall the two triangles themselves are the same (aka congruent). The tickmarks show that AB = DE and AC = DF.

-----------

Choice B

Unfortunately, we don't have info about whether the hypotenuse lengths are the same or not. We don't know if BC = EF is true or false. So we can't use the "H" in "HA". We rule out choice B.

HA = hypotenuse angle

Specifically, the "angle" refers to the acute angle.

Side note: we could use the pythagorean theorem to show that BC = EF, but I think your teacher wants you to use what is immediately available. So we cannot rely on this theorem.

-----------

Choice C

Like with choice B, we don't know anything about the hypotenuses. So we rule out this answer choice.

HL = hypotenuse leg

-----------

Choice D

LA stands for Leg Angle, where the angle is acute. We can use LA here because AB = DE is one leg pair (or we could use AC = DF). So that takes care of the "L" portion. The "A" portion is handled by the fact that angle B = angle E due to the arc markings. We cannot use the right angles when it comes to LA. This is because LA already applies to right triangles only. Put another way, if we didn't know that B = E, then we can't use LA.

-----------

Choice E

AAS = angle angle side

Note the order because it's very important. The side is not between the angles. We can use AAS because of these three facts

angle B = angle E
angle A = angle D
side AC = side DF

The side AC is not between the angles mentioned for triangle ABC. The side DF is not between the angles mentioned for triangle DEF.

-----------

Choice F

Again the order is important for SAS. The angle is between the sides. SAS can be used because

side AB = side DE (the first "S")
angle A = angle D (the "A" of "SAS")
side AC = side DF (the second "S")

Effectively, we just used LL here. If angles A and D were something else (let's say they were both 45 degrees), then we wouldn't use LL and instead SAS only. The LL rule is a special case of SAS which applies to right triangles only.

-----------

Once again, the abbreviations to write down in your notes and memorize are:

LL = leg leg
HA = hypotenuse angle (the acute angle)
HL = hypotenuse leg
LA = leg angle (the acute angle)
AAS = angle angle side
SAS = side angle side

The order is important with AAS and SAS. The first four rules only work for right triangles.