Explore Jim Wilson's problem set #6, choose one of the problems and do a writeup.
Given 3 line segments, j, k and l, if these are the medians of a triangle, construct the triangle.
Well, the first thing we should do is look at a sketch I provided using Geometer's Sketchpad.
Click here to view sketch
As you can see, I have provided line segments j,k and l. Since all three segments are the medians of a triangle, they form their own triangle, ABC. The first thing we need to do is to translate this triangle, so that when we are finished we will have both the new triangle and the median triangle to play with.
In order to translate triangle ABC, we will use the transform pull down menu, then the translate command. To see the translation, click on the action button provided.
Now we have a new triangle to work with, which is also dependent on our first triangle.
Since j,k and l are medians, each segment is parallel to the opposite side of the bigger triangle. So what we need to do is to construct the corresponding parallel lines. We can do this by selecting a point and it's opposite median, then choosing the construct pull down menu and selecting the parallel line command. So for example, we would select point C and segment k, then use the construct menu and the parallel line command. To see the parallel lines, click on the action button provided.
Now we have the correct lines to make our triangle. We must first construct the intersection points of lines p,q and r. We can then hide the parallel lines and we will be set to finish our construction. To see the intersection points, and the hiding of lines p,q and r, click on the action button provided.
Now, all that we have left to do is to construct the segments that connect points G,H and I. To see these lines, click on the action button provided.
The last step will be to hide triangle ABC, click on the action button provided.
There is the triangle which results in a median triangle called ABC.
To see that we are correct, you can move either of points A,B or C. The result will be triangle GHI moving right along with it.
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