**If the original triangle is equilateral,
then the triangle of median is equilateral. Will an isosceles
original triangle of medians? Will a right triangle always generate
a right triangle of medians? Under what conditions will the original
triangle and the medians triangle both be right triangles?**

**First let's look at an equilateral
triangle.**

**As you can see, that triangle of medians is also equilateral.
And we know from previous Geometry classes that the sides in the
smaller triangle are half the length of the original triangle's
sides.**

**Now let's look at the isosceles triangle.**

**This triangle of medians is also an isosceles triangle,
where the two sides of the original triangle that are equal are
opposite the two sides that are equal in the triangle of medians.**

**Now let's look at a right triangle. Before we look, I feel
that the triangle of medians will be a right triangle and the
right angle in the triangle of medians will be opposite the right
angle in the original triangle.**

**As we see I was right. So what conjectures can I make? Well
first of all inall of the cases we have seen, the triangle of
medians is a similar triangle. The sides opposite the sides in
the original triangles are half the length and the angles are
the same. Therefore the ratio is 2 to 1 for the original triangle
and the triangle of medians.**