Suppose that ca = 12, cb = 20, df = 6, and fe = 10. which additional fact would guarantee that the triangles are similar? a) ab = 24 and de = 12 b) ab = 30 and de = 18 c) ab = 12 and de = 24 eliminate d) m∠a = m∠d

A) AB = 24 and DE = 12

Step-by-step explanation:

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar. Then:

On the other hand:

So, the additional fact that would guarantee that the the triangles are similar is AB=24 and DE=12 given that:

So the three pairs of sides have the same ration, in consequence, the angles are also equal.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)