Using Similarity to Prove the Pythagorean Theorem

The Pythagorean Theorem is one of the most interesting theorems for two reasons: First, it’s very elementary; even high school students know it by heart. Second, it has hundreds of proofs. The proof below uses triangle similarity. Pythagorean Theorem In a right triangle with side lengths and and hypotenuse ,  the following equation always holds: .
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Properties of Similar Triangles Part 2

This is the third and the conclusion of the Triangle Similarity Series. The two prequels  are 1. Introduction to Similarity and 2. Properties of Similar Triangles (Part 1). *** In the previous post, we have investigated the properties of similar triangles. We have learned that corresponding angles of similar triangles are congruent. In this post, […]
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Properties of Similar Triangles Part 1

This is the second part of the Triangle Similarity Series.  The first part is Introduction to Similarity. In Introduction to Similarity, we have learned that similar objects have the same shape, but not necessarily have the same size. We drew a triangle using a graphics software zoomed it in and zoomed it out producing similar […]
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