SOLUTION: If triangle ABC is similar to triangle DEF, express AB in terms of other lengths. (There are two possible answers)

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Question 824277: If triangle ABC is similar to triangle DEF, express AB in terms of other lengths. (There are two possible answers)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Normally the order of the vertices used to name a triangle is not important. But when a statement about similar (or congruent) triangles is made, the order is meaning full.

So "triangle ABC is similar to triangle DEF" tells us more than just the fact that the two triangles are similar. The first letters in the names correspond to each other (so A corresponds to D), the second letters correspond (B corresponds to E) and the third letters correspond (C corresponds to F).

This also helps us figure out which sides correspond to which sides. AB corresponds to DE, BC corresponds to EF and AC corresponds to DF.

Since corresponding sides of similar triangles are proportional, then various ratios of the corresponding sides are equal. Since we're interested in AB we will start with a ratio of AB to its corresponding side from the other triangle:
AB%2FDE
Now we will write a couple more ratios of corresponding sides:
BC%2FEF
AC%2FDF

Because of the proportionality, all three of these ratios are going to be equal. So
AB%2FDE+=+BC%2FEF
Multiplying each side of this by DE we get:
AB+=+DE%2A%28BC%2FEF%29
This is one of the two possible answers.

Also,
AB%2FDE+=+AC%2FDF
Again we multiply by DE:
AB+=+DE%2A%28AC%2FDF%29
This is the other possible answer.