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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Squares, Triangles, and Van-Aubel’s Theorem

Problem In the figure, H is the midpoint of side BC of ΔABC. The points I and J are the intersection of the diagonals of square ABDE and square ACGF respectively, that is they are the centers of the square. Prove that IH and HJ are congruent and that angle IHJ is a right angle….

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Perpendicular Bisectors of Triangles

What is a perpendicular bisector? A perpendicular bisector of a line segment is a line that makes a 90-degree angle (a right angle) at the midpoint of a segment. In the figure, line b is the perpendicular bisector of line segment AB at C. This implies AC=CB and the measure of the angles at C…

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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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