Triangles
To begin this investigation one should construct an arbitrary triangle using Geometers SketchPad.
Now, lets consider the following:
What polygon is formed by connecting the midpoints of a triangle?
Another triangle
What conjectures can be formed concerning congruences, similarities, area and perimeter?
The midpoints form four congruent triangles.
Therefore, the area of each of the four congruent triangles
is ¼ the area of the original.
Each of the four congruent triangles is similar to the
original triangle.
The perimeter of the smaller triangle is ½ the
perimeter of the original triangle.
(click on the conjecture to see proof.).
Test the conjectures yourself!