Department of Mathematics Education
EMAT 6600
Triangles and Squares

Consider any triangle ABC. Construct a square to the outside of the triangle on each side.

Click here for a Geometer's Sketchpad script to generate this construction.

Select any two square centers and the midpoint of the other side of triangle ABC. Explore the triangle formed by these three points.

Conjectures?

Proof?

Explore the relationship of two segments, one being defined by a vertex of the triangle and the center of the square on the opposite side and the other being defined by the centers of the squares on the sides adjacent to the vertex.

Note that there are three pairs of such segments.

Prove that the three lines from the vertices to the centers of the squares on the opposite sides are concurrent.

Explore the same relationships when the three squares on each side are constructed toward the interior of the triangle:


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