Which theorem or postulate proves the two triangles are similar? a. sas theorem b. sa postulate c. sss theorem d. aa postulate

Similarity cannot be proven by side lengths.  Only congruency can be proven by equal length sides.  No matter how long 2 adjacent sides are in 2 different triangles, the angles between them can still be the same.  So we are looking for a theorem or postulate involving angles only.  We have an angle in each triangle given to us a being congruent to one another.  We also have the fact that where those 2 intersecting lines cross there are vertical angles.  So those by definition of vertical angles are also congruent.  So we can prove them similar by AA.

For the diagram above, we have 2 angles that are equal. this makes AA.
Then we have two sides given to check the factor ratio. 

So, form the choices given the correct answer is D. AA Postulate.

This means 2 angles from both triangles are equal and the ratio of sides is the same.
That is; 27/11 = 9/(11/3)