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The applet below shows a median of triangle ABC. Drag any of the vertices to change the shape of the triangle.
The Show Median buttons show the three medians of the triangle from each of the vertices. The Show Measurements button displays the lengths of the medians, and the Show Sum Relationships button displays a graphic that shows the relationship between the sum of the side lengths, the perimeter (p), and the sum of the medians.
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Drag points A, B, and C to adjust the size and shape of the triangle. Use the Show Median buttons to draw each of the three medians of the triangle.
- Do you notice anything special about the three medians of the triangle? In particular, what do you observe about the intersections of the medians? Do you think this will always be the case? Adjust the triangle to test your conjecture.
- Do some research. What is the name of the point where the three medians meet?
Click on the Show Measurements and Show Sum Relationships buttons. The lengths of the medians will be displayed, as well as a graphic showing the relationship between the perimeter (p) of the triangle and the sum of the medians. (Notice that the perimeter is equal to the sum of the side lengths, AB + BC + AC.)
- How large can you get the bottom line to be, with respect to the perimeter?
- How small can you get it to be?
- Can you ever get the sum of the medians to exactly equal ¾ the perimeter of the triangle? Adjust the vertices of the triangle to find out.
- Can you get the sum of the medians to exactly equal the perimeter? Adjust the vertices of the triangle to find out.
- What conclusion can you make about how the sum of the lengths of the three medians is related to the perimeter of the triangle?
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