Department of Mathematics Education
J. Wilson, EMT 669

1. Given a triangle ABC, find a point D such that line segments AD, BD, and CD trisect the area of the triangle into three regions with equal areas.

Define D and prove that the triangle is divided into three regions of equal area. Show a construction for finding D.

2. Given a triangle ABC, and given a point E. find points B' and C' such that line segments AE, B'E, and C'E trisect the area of the triangle into three regions with equal areas.

Show a construction and prove that it divides the triangle into three regions of equal area. Are there restrictions on the location of E within or on the triangle?

3. Given a triangle ABC. Construct two line segments parallel to the base BC to divide the triangle into three regions with equal areas.

Prove that the construction divides the triangle into three regions of equal area.

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