Example 5. The area of the median triangle is 3/4 of the area of the original triangle.
The solution is based on the fact established in Example 4 and on two transformations. First we use a translation of two of the medians to build the median triangle. The second transformation is shearing (also known as the 2D case of Cavalieri's principle) of the three triangles forming the median triangle.
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Example 6. The Law of Cosines
Like in Example 3, the animation in this applet creates a good visualization of the proof, but in order for the proof to be completed it needs to be supplemented by a couple of equations. See f.[4]
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Example 7. Pythagorean Theorem
The proof of the Pythagorean Theorem follows from the Law of Cosines.
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