Question 157829: A triangle has sides whose lengths are 2,12, and 13. A similar triange could have sides with lengths of:
1) 3,13,14
2) 4,24,26
3) 3,4,5
4) 10,24,26
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! if the triangles are similar, then the angles are equal and the corresponding sides are proportional by the same ratio for each.
your original triangle is 2,12,13
3,13,14 doesn't look good because the ratios are not the all the same.
4,24,26 looks good because 4/2 = 24/12 = 26/13 = 2. all the ratios for the corresponding sides are the same.
3,4,5 doesn't look good because the ratios are not all the same. 3/2 does not equal 4/12.
10,24,26 doesn't look good because the ratios are not all the same. 2 of them are the same (24/12, 26/13) but the 3d is not (10/2).
it's not enough that 2 of them are the same.
they all have to be the same.
if triangle ABC is similar to triangle DEF, all the angles have to be equal and all the corresponding sides have to be proportional by the same ratio.
let side a correspond to side d,
let side b correspond to side e.
let side c correspond to side f.
then a/d must = b/e must = c/f.
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