Exploring Triangles and Their Medians
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 90o.† The squares of the two legs of the triangle (ie. the sides that form the 90o) 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.