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Is it true for every triangle that the longest median is to the shortest side and the shortest median is to the longest side?

Sekhar0210
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Oct 29 '22 at 05:34
  • This website provides two proofs: https://mathvox.com/geometry/triangles/chapter-10-the-median-of-a-triangle/which-side-of-a-triangle-does-the-smallest-median-correspond-to-proof-1/ – Bumblebee Oct 29 '22 at 05:50
  • @Ajay Thanks. I will need to think through step 3 of the proof .... in a triangle, angle opposite largest side is largest .... can this comparison also hold between two different triangles? If a side of one triangle is larger than a side of another triangle, will opposite angle of 1st triangle also be larger than opposite angle of 2nd triangle? There is also the condition that other two sides are respectively equal, which makes it easy to compare when when I start with two congruent triangles, yet I will need to clear my doubts more convincingly. Thanks again. – Sekhar0210 Oct 30 '22 at 15:17
  • @Ajay, the 2nd proof was more helpful.

    I wonder why this property is not more commonly available discussed in text-books, I did search quite a bit .... while side opposite largest angle is largest and side opposite smallest angle is smallest is part of most text-book, I did not find the relation ... median to longest side is shortest and median to shortest side is longest ... very easy to search for.

     – Sekhar0210 Oct 30 '22 at 15:23

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