Chapter 8, Problem 33RP

To determine

To prove:The product of the measures of the altitude and the hypotenuse is equal to the product of measures of the legs of the right triangle

Explanation of Solution

Given information:

If an altitude is drawn to the hypotenuse of a right triangle

Formula used:

Compare the corresponding sides of the triangles

Proof :

In the figure below, AD is the altitude on Hypo AC

  

Since triangles ABC and ADB are similar, we have

  $\begin{array}{l}\frac{\text{BC}}{\text{AC}}=\frac{\text{BD}}{\text{AB}}\\ \Rightarrow \text{AC×BD}=\text{BC×AB}\end{array}$

IT gives,

Product of measures of altitude and Hypo of the right angle = Product of measures of legs of right triangle

Hence proved