Based only on the information given in the diagram which congruence theorems or postulates could be given as reason why abc=def

HL

SAS

SSS

Step-by-step explanation:

Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.

For HA to work we must have been given something else about one of those angle (besides the 90 degree one).

Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.

We can't use AAS.  We only know something about one angle per each triangle due to the markers.

LA? Needed another angle besides the 90 degree one.

All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.