The Department of Mathematics Education

# ASSIGNMENT 6

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.

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.

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.