**The Department of Mathematics Education**

# ASSIGNMENT 6

### Explorations with Geometry's
Sketchpad

By Godfried Lawson

**In this assignment I will check if the following assumption
is true or false:**

**If the original triangle is equilateral, then the triangle
of medians is equilateral.**

**Then I check the following:**

**Will an isosceles original triangle generate and isosceles
triangle of medians? Will a right triangle always generate a right
triangle of medians? What if the medians triangle is a right triangle?
Under what conditions will the original triangle and the medians
triangle both be right triangles?**

Theorem: A segment joining the midpoints of two
sides of a triangle is parallel to the third side and half its
length. Each of the 3 triangles are congruent isosceles
by definition of midpoints for all 3 sides. Each triangle is congruent
by SAS. The 3rd sides are congruent by CPCTC. This makes the median
triangle equilateral by virtue of three congruent sides.

Click **here** to see the animation

T.

Theorem: A segment joining the midpoints of two sides of a
triangle is parallel to the third side and half its length.
Prove the two triangles at the base congruent by SAS. Using parallel
lines and corresponding angles you can find and prove the triangles
congruent or an isosceles triangle congruent to the others.

Click **here** to see
the animation

Theorem: A segment joining the midpoints of two sides
of a triangle is parallel to the third side and half its length.
Using parallel lines and corresponding angles you can find and
prove the right angles. Using alternate interior angles you can
prove the first acute angle. The second angle is found by subtraction.
By virtue of HA, you can prove 3 triangles congruent and the remaining
triangles congruent by using another side.

Click **here** to see
the animation

**Return**