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Geometric Mean-Altitude Theorem 2The altitude to the hypotenuse to a right triangle intersects it to that the length of each leg us the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuseBACB=CBBD ABCA=CAAD 𝐂𝐁=𝐁𝐃×𝐁𝐀 𝐂𝐀=𝐀𝐃×𝐀𝐁 Geometric Mean-Altitude Theorem 1The length of the altitude to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse.CABD𝐀𝐃𝐂𝐃=𝐂𝐃𝐃𝐁 𝐂𝐃=𝐀𝐃×𝐃𝐁 Right Triangle Similarity TheoremThe altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.CABDABC ~ ACD ~ CBD Parts of a right triangle incorporated with the altitudeCLeg adjacent to DBLeg adjacent to ADABDSegments of the hypotenuse AD and DB We can see that the three triangles are similar to each other.

We orient the three triangles to see the them clearer.BigSmallMedium There are a three triangles in the figure below. This divides the original triangle into two smaller right triangle: ΔBDC This divides the original triangle into two smaller right triangle: ΔDCA The circumradius of a right triangle is equal to half of the hypotenuse, or the median to the hypotenuse.This divides the original triangle into two smaller right triangle: Using similarity, it is possible to derive several formulas relating the sides, the hypotenuse, and the median. It can also be calculated using half of the product of the median to the hypotenuse and the hypotenuse. The area of the triangle can be calculated using half of the product of the lengths of the legs.

If the lengths of the legs and hypotenuse are integral, they are said to form a Pythagorean triple. This triangle is analogous to an equilateral triangle cut in half down the middle.

This triangle is analogous to a square cut in half along its diagonal.Īnother one of these is the triangle, which has sides in the ratio of. One of these is the isosceles triangle, where the hypotenuse is equal to times the length of either of the legs. There are several right triangles with special properties.