Question

Prove: In an equilateral triangle the three medians are equal.

Answer 1

The three medians are all equal in the case of equilateral triangles because the distance from the vertex of one angle to the side directly opposite it is always same for each angle.

Answer 2

LOL HUH?

Answer 3

In that diagram, just use the distance formula(\[distance=\sqrt{(x2-x1)^{2}+(y1-y2)^{2}}\]
to calculate the length of each median. You will find that they are equal.
Do u get it? Do u need a geometrical solution?

Answer 4

this is how they want it answered AC= a _ _ _ _ and BD= _ _ _ _ ^2

Answer 5

\[AC= \sqrt{a^2+b^2}\]
\[ AB= 2a \]
In an equilateral triangle, AB=AC
from this we find
\[ b= a \sqrt{3} \]
which we will need to show that the medians all have the same length