Let's say you have a triangle. If you measure from the midpoint of one line to the midpoint of another line,?

Draw triangle ABC

Let X = point 1/10 th of the way between A and B

Let Y = point 1/10 th of the way between A and C

You want to determine if length of XY = 1/10th length of BC.

Compare triangle ABC to triangle AXY

AX/AB = 1/10 = AY/AC and ∠BAC = ∠XAY

So triangles ABC and AXY are similar (by SAS)

Since triangles are similar

XY/BC = AX/AB = 1/10

XY = 1/10 BC

Yes, XY is indeed 1/10th of BC.

No, that makes sense. Actually, that is a property of similar triangles. You can prove that when you make that line, you make another triangle that is similar to the larger one. A result of that is the proportionality of sides. So yeah, it can work for almost any value, from a 6th to a tenth to a millionth.

Sorry....it's just not making sense to me what you mean.

If it's an equilateral triangle, perpendicular bisectors of each leg meet at the centroid of the triangle, and you're right (I thin k) that bisecting one leg, and going to the midpoint of the opposite leg is the half way point of that leg, but I don't know hat you mean from there.

This is very unclear, But by a poorly drawn sketch that i just did i think u r right