Chapter 9.3, Problem 20PSC

To determine

To prove: That the product of the measures of the legs of right triangles is the product of hypotenuse and altitude.

Explanation of Solution

Given information :

There is a right-angle $\Delta ABC$

Formula used :

Ratios of corresponding sides are equivalent.

Proof :

Given a right-angle triangle

  

  $BD$ is an altitude on hypotenuse $AC$

  $\angle ABC=\angle BDA=90°$

In triangles, $ABC\text{ and }ADB$ , we have

  $\angle ABC=\angle BDA=90°$

  $AB$ is a common side.

  $\begin{array}{l}\frac{AB}{AC}=\frac{BD}{BC}\\ AB\times BC=AC\times BD\end{array}$

  $\text{Product of legs = Product of altitude and hypotenuse}$

Hence proved