Given two triangles, if their hypotenuse are congruent, and one pair of their legs are congruent then the two triangles are congruent. In this post, we are going to prove this theorem. In the figure below, ABC and DEF are right triangles with right angles at C and F, respectively. It is given that and . […]

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# Posts by Math Proofs

## Proof that for all real numbers a, |-a| = |a|

We can think of the absolute value of a number as its distance from 0. So, the absolute value of a, which is denoted by is always greater than 0. In this post, we are going to prove that for all real numbers a, |-a| = |a|. There are two possible cases: and $latex b […]

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## Derivation of the Equation of the Parabola

A circle is a locus of points whose distance from a fixed point is a constant. A parabola can also be described as a locus of points whose distance from a fixed point and a fixed line not passing through that point is a constant. An example of a parabola is shown below. In the figure […]

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