Tuesday, March 11, 2014

Mario's Parallel Coins

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While playing a computer version of the classic Super Mario Bros. that I found online, I found a secret underground area, which is pictured above. In the underground area, I noticed that the coins seemed to be perfectly parallel to each other.

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And, as it turned out, I was correct. By placing a point at the center of each coin and drawing lines between them, the coins formed lines parallel vertical lines and parallel horizontal lines. One can prove them parallel because the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are congruent. Because all of the angles formed by the intersections of the vertical and horizontal lines all have a measure of 90 degrees, they are perpendicular. This shows something important about coplanar horizontal and vertical lines: they are always perpendicular to each other. (~JC1)

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