**Exploring Triangles and Their Medians**

**Sharon Sewell**

This is another exploration of Geometer’s
Sketchpad and its uses in the classroom. This will be a study of the relationship
between a triangle and the length of its medians. We will create several
different kinds of triangles and compare the lengths of their medians to
the angles and the length of the sides.

An isosceles triangle has two equal sides and two angles that are equal.

The medians are found when a line segment is drawn from a vertex to the midpoint of the opposite side. Thus the medians of the triangle are represented by the dashed lines. When the dashed lines are measured they are found to be as shown. Click here. Isosceles. This would then create another isosceles triangle. You can play with the sketchpad and see if this is always true that when the main triangle is isosceles then the medians will form an isosceles triangle.

The right triangle presents a completely
different picture. A right triangle is formed when one of the angles in
the triangle is 90^{o}. The squares of the two legs of the triangle
(ie. the sides that form the 90^{o}) added together equal the square
of the hypotenuse. When we draw in the medians of a right triangle we
find that another right triangle cannot be formed by the median lines.
You can play with the sketchpad and see if this is always true that when
the main triangle is a right triangle then the medians will not form another
right triangle. Click here to access the right triangle.

Now if we have a triangle whose medians form a right triangle then the main triangle forms another right triangle. You should play with the sketchpad and see if this is always true that when the medians form a right triangle then the triangle formed by using the main triangles as the medians of the second triangle a right triangle is formed. Click here to access the right triangle median.

This seems to be a wonderful tool for exploring the relationship between the medians and the sides of a triangle. The students will be better able to see how when one changes then the other shifts also. Please note the measurements of the triangles were as close to perfect as the program would let. But it does enable us to see what is going on. This is one of the limitation of the program. It does not allow for perfection.