1)
Determine which postulate proves the following
triangles are congruent. (ASA,SSS, AAS, ect)

≅

See below.

Step-by-step explanation:

If we rotate the shape on the right 90 degrees counterclockwise we see they fit together, because they are congruent. They are exactly equal in size and shape - that's what congruent means.

So the following angles are equal in measure:

m < A = m < R

m < B = m < S

m < C = m < P

m < D = m < Q.

Corresponding sides are also equal in length:

Sides AB = RS

BC = SP

CD = PQ

AD = RQ.

Note:  in the US the symbol ≅ is used for equality of sides. I think it means 'is congruent to'. (I'm from the UK).