Triangles - Under Construction
(the triangles - not the website)
by  Jackie Ruff

Construction 1 - For this construction we are given two sides of a triangle and the median to the third side.  If we consider the sample triangle below, it will show us the way to construct a triangle with this given information.

 We are given two sides, b and c, and the median to the third side.

Construction 2 - For this construction we are given two angles and the perimeter of a triangle.

 GSP File

Construction 3:  Construct a triangle given the three medians.

 We are given the three medians of a triangle.  We also know that the medians of a triangle are concurrent in a point whose distance to a vertex is two-thirds of the length of the median from that vertex - a fact we will use in this construction. To finish, we just construct the segments AC and BC and we have constructed the triangle with the given medians.  Here is a link to a GSP file to see that the construction holds as the lengths of the medians are changed.

Construction 4:  Construct a triangle given two sides and the angle opposite one of the sides.
 Here is a link to a GSP file for this construction.

Construction 5: Construct a triangle given two sides and the altitude to the third side.

 Given two sides and the altitude to the third side: Here is a link to a GSP file for this construction.

Construction 6:  Construct a triangle given a side, the median to that side, and another median.

If we consider our sample triangle with the given information marked in red we will see a triangle that we can construct by SSS.

 Here is a link to the GSP file for this construction.

Link to free clip art used on this webpage.