If angle a is congruent to itself by the reflexive property, which transformation could be used to prove δabc ~ δade by aa similarity postulate?

translate triangle abc so that point c lies on point d to confirm ∠c ≅ ∠d.

dilate δabc from point a by the ratio segment ad over segment ab to confirm segment ad ~ segment ab.

translate triangle abc so that point b lies on point d to confirm ∠b ≅ ∠d.

dilate δabc from point a by the ratio segment ae over segment ac to confirm segment ae ~ segment ac.

answer: choice 3

translate triangle abc so that point b lies on point d to confirm that angle b is congruent to angle d

explanation:

the triangles are congruent by the aa (angle angle) similarity theorem only if we can find a pair of angles that match up and are congruent. we're already given that "angle a is congruent to itself" (more technically: angle bac = angle dae). so this is the first pair of angles we need.

the second pair of angles could be sliding the triangle up so that point b overlaps point d; also the angles match up as well to confirm they are the same measure. if we can do this, then we have shown that angle b is congruent to angle d. an alternative is to slide triangle abc to the right so that angle c lines up with angle e. though this answer choice is not listed.

side note: choice 2 and choice 4 would only apply if you are trying to prove similarity through the sas similarity theorem.

the image of (6, 9) under a dilation is (4, 6). the scale factor is