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.

d

gimmee one of those gold crowns!

~coco

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560