When one side of triangle is makes an angle of 90 degrees, then given triangle is called as a Right Triangle means each right triangle has 90 degree angle. As we all know that geometric Mean of 2 Numbers are √ (a * b), where ‘a’ and ‘b’ are two numbers. Now we will discuss how to find out geometric mean in right Triangles.
altitude to hypotenuseBack to Top
Now we will proceed to Altitude to the hypotenuse.
In the given figure 1, the Right Triangle PQR has altitude QS that is drawn to the hypotenuse PR.
By using the AA Similarity Postulate this theorem cannot be shown easily.
Now we will see the Theorem of altitude to the hypotenuse. In the given figure, the altitude plot to the hypotenuse of a right triangle which creates two similar right Triangles, in the given triangles each are parallel to the original right triangle and analogous to one another.
Figure 2 defines the three right triangles created in Figure 1. All these triangles are drawn in such a way that equivalent parts of triangle are easily known.
In the given figure ‘PQ’ and ‘QR’ are legs of the original right triangle; PR is the hypotenuse in the original right triangle; QS is the altitude drawn to the hypotenuse; PS is the segment on the hypotenuse touching leg PQ and SR is the segment on the hypotenuse touching leg QR.
As we know that these all triangles are related to each other, and the ratios of all pairs of corresponding sides are same.