CK12 - Geometry

Theseare all true by the trianglesimilaritypostulate.

Now, usingsimilartriangles,we can set up the followingproportion:

and

Puttingtheseequationstogetherby usingsubstitution,

factoringthe right handside,

but notice , so this becomes

.

We havefinishedprovingthe PythagoreanTheorem.Thereare hundredsof otherwaysto provethe
PythagoreanTheoremand one of thosealternativeproofsis in the exercisesfor this section.

MakingUse of the PythagoreanTheorem

As you knowfrom algebra,if you haveone unknownvariablein an equation,you can solveto find its value.
Therefore,if you knowthe lengthsof two out of threesidesin a right triangle,you can use the Pythagorean
Theoremto find the lengthof the missingside,whetherit is a leg or a hypotenuse.Be carefulto use inverse
operationsproperlyand avoidcarelessmistakes.

Example 2

Whatis the lengthof in the trianglebelow?

Use the PythagoreanTheoremto find the lengthof the missingleg,. Set up the equation

, letting and. Be sure to simplifythe exponentsand rootscarefully, rememberto use inverse