The legs of the triangleaboveare inchesand inches.The hypotenuseis inches.So, ,, and. We can substitutethesevaluesinto the formulafor the PythagoreanTheoremto verifythat
the relationshipworks:
Sinceboth sidesof the equationequal , the equationis true.Therefore,the PythagoreanTheorem
workedon this right triangle.
Proofof the PythagoreanTheorem
Thereare manywaysto provethe PythagoreanTheorem.One of the moststraightforwardwaysis to use
similartriangles.Start with a right triangleand constructan altitudefrom the right angleto the oppositesides.
In the figurebelow, we can see the followingrelationships:
Proof.
- Given: as shownin the figurebelow
Prove:
First we start with a trianglesimilaritystatement: