Geometry Review, Part I

  1. A triangle inscribed in a semicircle is a right triangle.

In the picture below we want to show that angle is a right angle. One way to see this is to take advantage of Cartesian coordinates: Here we've identified our semicircle with the top half of the graph of .

To check that is a right angle, we will show that the Pythagorean theorem is satisfied for this triangle (with the diameter of our circle as the hypoteneuse of the right triangle). In terms of our coordinates:

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Neal Carothers -