Triangle inside a Triangle

Geometry Level 4

If you have a triangle with sides $A>B>C$

and a smaller triangle with sides $a>b>c$ ,

where $a<A$ , $b<B$ , and $c<C$ ,

will the smaller triangle always fit inside the larger one?

Yes, the smaller triangle can always fit completely inside the larger triangle No, sometimes the smaller triangle must lie partly outside the larger triangle Yes, but sometimes the smaller triangle must touch the larger triangle

1 solution

Jeremy Galvagni
Jun 9, 2018

The small triangle clearly does not fit. If you need to convince yourself further you can find the smallest altitude of each triangle.

Triangle inside a Triangle

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