Right Triangle from Hypotenuse

﻿This is the construction of a right triangle from its hypotenuse. We know that a right triangle has one right angle and that the side across form the right angle is the longest side. This longest side is called the hypotenuse. To construct a right triangle from its hypotenuse we first needed to have a hypotenuse. First I constructed circle C. Then I constructed the diameter of circle C, segment AB. Next I constructed point D on the circle. Next I connected points A,B,D with segments AB, AD, DB. Now we can see that we have triangle ADB. Using the angle measure tool we can see that is a right angle. We also know that  is a right angle by the inscribed angle theorem. The inscribed angle measures half of the arc it is inscribed in. The arc that is inscribed in is a semicircle. This means that it measures . Therefore  and the measure of  is . This concludes that triangle ADB is a right triangle. We can move point D around the circle and we notice that remains a right angle and the triangle remains a right triangle with a hypotenuse AB.