Metric Relationships in a Right Triangle
Properties
Consider the following right triangle:
- The Pythagorean theorem:
[latex]({\textrm{m}{\overline {\textrm{BC}}}})^{2}[/latex] = [latex]({\textrm{m}{\overline {\textrm{AB}}}})^{2}[/latex] + [latex]({\textrm{m}{\overline {\textrm{AC}}}})^{2}[/latex] [latex]\space[/latex]
- The mean proportional:
[latex]({\textrm{m}{\overline {\textrm{AC}}}})^{2}[/latex] = m[latex]\overline {\textrm{BC}}\space \times [/latex] m[latex]\overline {\textrm{HC}}[/latex] [latex]({\textrm{m}{\overline {\textrm{AB}}}})^{2}[/latex] = m[latex]\overline {\textrm{BC}}\space \times [/latex] m[latex]\overline {\textrm{HB}}[/latex] [latex]({\textrm{m}{\overline {\textrm{AH}}}})^{2}[/latex] = m[latex]\overline {\textrm{HB}}\space \times[/latex] m[latex]\overline {\textrm{HC}}[/latex] [latex]\space[/latex]
- The product of the measures of the right angle's sides:
m[latex]\overline {\textrm{AB}}\space \times[/latex] m[latex]\overline {\textrm{AC}}[/latex] = m[latex]\overline {\textrm{BC}}\space \times[/latex] m[latex]\overline {\textrm{AH}}[/latex]