Proof that the Solution of 3^x = 8 is Irrational

In this post, we discuss another example of proof by contradiction. We are going to prove that the solution of the equation 3^x = 8 is irrational. Theorem The solution to the equation is irrational. Proof In proof by contradiction, we assume the opposite of the theorem and then find a contradiction somewhere in the […]
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The Proof of the Hypotenuse Angle Theorem

Last month, we have discussed the proof of the Hypotenuse Leg Theorem. It states that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another triangle, then the two triangles are congruent. In this post, we are going to discuss a related theorem on right triangles, […]
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The Proof of the Right Triangle Altitude Theorem

The geometric mean of two positive integers and is . In this post, we are going to show the relationship between geometric mean and the relationships among the sides and altitude of a right triangle. The Right Triangle Altitude Theorem In a right triangle, the altitude to the hypotenuse is the geometric mean of the […]
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