Jeff asks the teacher if asa is also a similarity criterion. the teacher says yes but it isn't needed, why isn't it needed ?

ASA means that we have two angles and the lenght of the side between them.

But as you know, the sum of the 3 interior angles of a triangle must add up to 180°

So ASA is equivalent to the AA criterion (where we know two interior angles), with only knowing two angles we have enough to see if two triangles are similar, so actually knowing the length of the side is not needed.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".