leahhhmorgannn
  • leahhhmorgannn
Triangle LMN has been dilated to form triangle L'M'N'. What is the least amount of information needed to determine if the two triangles are similar? Segments LN and L'N' are congruent, and segments MN and M'N' are congruent. Angles M and M' are congruent, and angles N and N' are congruent. Segment BC=B'C', segment LN=L'N', and angles M and M' are congruent. Angle N=N', angle B=B', and segments BC and B'C' are congruent.
Mathematics
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SOLVED
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katieb
  • katieb
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leahhhmorgannn
  • leahhhmorgannn
I know this has something to do with the Angle-Angle Postulate, at least I think... but I'm not sure which answer it would be.
anonymous
  • anonymous
the triangles can be similar by: 1) 2 angles 2) if three sides of 1 triangle are proportional to the three sides of second one 3) if two sides of one triangle are proportional to the two sides of second and angles between them are congruent
leahhhmorgannn
  • leahhhmorgannn
I was thinking it would be the last one based on the AA Postulate... would that be right?

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anonymous
  • anonymous
i thought B because the segments don't need to be congruent - you already have two congruent angles in last choice, so you don't need segmens at all.
leahhhmorgannn
  • leahhhmorgannn
But based on one of the things you said, C sounds right too.
anonymous
  • anonymous
why? |dw:1447294459995:dw| angle M (M') are not between sides BC (BC') and LN (LN')
anonymous
  • anonymous
actually I don't see sides BC at all in these triangles
leahhhmorgannn
  • leahhhmorgannn
Well M is between L and N though. But I see what you're saying. I guess this is just a confusing question for me. Okay, so it's NOT C or D. Why couldn't A be right? Just ruling them all out.
anonymous
  • anonymous
you see, they ask the least information, but segments may and may not be congruent - they just need to be proportional. they can be congruent also. and besides there aren't angles. there should have been N=N'
anonymous
  • anonymous
the angles MUST be here, but sides don't have to be congruent
leahhhmorgannn
  • leahhhmorgannn
Okay. So any answer that didn't include angles would automatically be wrong?
anonymous
  • anonymous
no. if one triangle has 3 sides proporional to the 3 sides of another, they are also similar
anonymous
  • anonymous
so here they are (all 3 rules) 1) |dw:1447294936449:dw| 2) |dw:1447294983399:dw| 3) |dw:1447295011299:dw|
leahhhmorgannn
  • leahhhmorgannn
Okay. It makes more sense visually to me. Thanks for that.
anonymous
  • anonymous
np :) so the final answer is B. there are two angles, which is enough to determine if the triangles are similar
leahhhmorgannn
  • leahhhmorgannn
Thanks so much for all your help!
The.Lit.Owl_23
  • The.Lit.Owl_23
the answer to the question on the top is B.

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