The Area of the Median Triangle - Dynamic Proof

Let ABC be a given triangle. The triangle with sides equal to the medians of ABC is called the Median Triangle.
We will show that the area of the median triangle is 3/4 of the area of the original triangle ABC.

•  Drag the two sliders to the end to construct the median triangle by translating the medians.

To rearrange the area of the median triangle:

• Click the Rearrange checkbox. This will show a green point at the vertex of the median triangle. 
•  Drag the green point to C.
•  Drag the green point at B to M_c. 
• Drag the green point at M_a to M_c. 

Irina Boyadzhiev, 29 January 2014, Created with GeoGebra

Download applet
Irina Boyadzhiev's  GeoGebra Applets