Question

I need help with a triangle- There is a link with the picture included:
Find LM
https://static.k12.com/eli/bb/343/4_23944/2_15030_6_23950/99096c966048557c059b5bc1ba6beb5aa918efc4/media/d8821a1d4801fdbfbb41ce588ccf518417499530/mediaasset_649792_1.gif

Answer 1

For any triangle, the smallest angle is always opposite the smallest side, and the largest angle is always opposite the largest side.
So look at your diagram to find the correct answer.

Answer 2

Thanks

Answer 3

In geometry, I we do not make assumptions based on figures.
Even if an angle in a figure looks like a right angle, we cannot assume it to be so.
We know an angle is a right angle if we are told so, or if we have information that can lead us to that conclusion, such as perpendicular lines.
We don't know anything about angles MPL and MPN. We cannot conclude they are right angles.
We are not told lines MP and LN are perpendicular.
Based on only the information given, we cannot calculate the length of LM.

Answer 4

Yeah I know but my teachers do stuff like this in every problem. If you were to assume the Angles MPL and MPN were right angles, could you find the answer?

Answer 5

@Error1603 response does not help becasue we don;t know any angle measures.

We don't know that triangles MPL and MPN are congruent, and we don't have enough info to lead us to conclude they are, so we cannot determine the length of LM.

Answer 6

Oh, I see.
If those angles are right angles, then the triangles are congruent by SAS.
Then LM and NM are congruent by CPCTC, so just like the length of NM is 11, the length of LM is also 11.

Answer 7

@mathstudent55 Thank you!