Category: Geometry

Four equal triangles problem

  Challenge yourself with this triangle problem. Squares were constructed on each side of triangle ABC. The free points of the squares were connected forming three more triangles. It is claimed that all the four triangles have equal area. Do they? Show that they do or don’t. Hints: Make a simpler problem. Use an isosceles triangle…

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Which rectangle has a bigger area?

ABCD is a square and G is a point on its diagonal. Obviously, the two colored rectangles have equal area: ab.   What about in the figure below? Problem: ACDB is a rectangle. E is a point on the diagonal.  Which rectangle has a bigger area? GEIA or FEHD? Answer The diagonal divides a rectangle…

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