# Metric Relationships in a Right Triangle

## Metric Relationships in a Right Triangle

Relationships between the measures of various segments in a right triangle.

### Properties

Consider the following right triangle:

$$({\textrm{m}{\overline {\textrm{BC}}}})^{2}$$ = $$({\textrm{m}{\overline {\textrm{AB}}}})^{2}$$ + $$({\textrm{m}{\overline {\textrm{AC}}}})^{2}$$
$$\space$$

$$({\textrm{m}{\overline {\textrm{AC}}}})^{2}$$ = m$$\overline {\textrm{BC}}\space \times$$  m$$\overline {\textrm{HC}}$$
$$({\textrm{m}{\overline {\textrm{AB}}}})^{2}$$ = m$$\overline {\textrm{BC}}\space \times$$ m$$\overline {\textrm{HB}}$$
$$({\textrm{m}{\overline {\textrm{AH}}}})^{2}$$ = m$$\overline {\textrm{HB}}\space \times$$ m$$\overline {\textrm{HC}}$$
$$\space$$

• The product of the measures of the right angle’s sides:

m$$\overline {\textrm{AB}}\space \times$$ m$$\overline {\textrm{AC}}$$ = m$$\overline {\textrm{BC}}\space \times$$ m$$\overline {\textrm{AH}}$$