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THE TRIANGLE WITH LENGTHS EQUAL TO THE MEDIANS OF A GIVEN TRIANGLE HAS AN AREA 3/4 THE AREA OF THE GIVEN TRIANGLE

The three medians of the triangle are shown in red. When you click on [show objects] the reflection of the triangle about one of the midpoints is drawn. Note that at this point we see 8 triangles with equal area which make up twice the area of the original triangle.

By clicking in the second box, you can see the triangle with sides equal to the three medians by a parallel tanslation of two of the medians. Can you see that it has an area equal to three of the eight small triangles?

You can adjust the size of the triangle by clicking and dragging any of the points in red. You can reset the sketch to its original form by clicking {refresh} on your browser.

Back to medians

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med3_4