Question

Help!!! Medal and Fan!!!!


The two triangles below are similar. What is the similarity ratio of ΔDEF to ΔABC?

Answer 1

Grab the equivalent side of one of the triangles and place it on top of the ratio and the other on the bottom.
\[\frac{ \triangle DEF }{\triangle ABC }\]

Answer 2

That way you can see the factor difference.

Answer 3

Im confused ...

Answer 4

Nvm so i have three 4s on top n one 8 and two 12s on bottom, correct?

Answer 5

Looks like the side AC is equivalent to the side FD on the smaller triangle so you can find the similarity ratio by placing the side of the bigger triangle on the top of your ratio and the equivalent side of the smaller triangle on the bottom.

Answer 6

So if sides AC and FD are equivalent you will have:\[\frac{ AC }{ FD }\]

Answer 7

Plug in your values and solve for the similarity ratio.

Answer 8

I got option 3:1?

Answer 9

Yes that could also be a possibility if you say sides BC and FD are equivalent which would be more accurate.

Answer 10

So im right

Answer 11

Or your saying its an option thats valid

Answer 12

Yes, if you say those 2 sides are equivalent.

Answer 13

oh ok but were saying here that AC and Fd are equivalent

Answer 14

Yes so if that were the case you would have a different ratio.

Answer 15

ok umm let me do the math again

Answer 16

Being that AC and Fd are equivalent i got 2:1?

Answer 17

Yes, that would be the ratio of the triangle ABC to DEF but your question is asking for DEF to ABC.

Answer 18

So you can take the reciprocal of that value and you will have DEF to ABC.

Answer 19

I think the question as posted is ambiguous.
There is no statement (unless you omitted it) that helps us identify which side is the corresponding side to which.
So the factor could well be 4/8=1/2 or 4/12=1/3.
Does the question say something like:
\(triangle ABC~is~ similar~ to~ DEF\)
in which case we know that AC corresponds to DF.
Without other indication, the question is ambiguous.

Answer 20

Thank you @mathmate. That clarification is important and that is why we could not determine the corresponding side.

Answer 21

So the reciprcol would be 1:2

Answer 22

Yes, if FD is equivalent to AC which may not be the case as mathmate pointed out.

Answer 23

Ughh i suck at this :(

Answer 24

AC may or may not be equivalent to DF this is the assumption we are making but yes if they are you are correct and you did great and most of it on your own so you definitely do not.

Answer 25

If there is nothing missing from the question, I would take a chance for AC~DF, i.e. factor = 4/8, based on the fact that the question mentioned the triangles in that order.

Answer 26

Thanks :) im just stumped on what the answer is

Answer 27

Theres not thats all they gave me and the picture

Answer 28

It's ok. Everybody is human, so is the person writing the question.

Answer 29

What do you mean by that

Answer 30

everyone makes mistakes your not the only one:)