Table of ContentsClick on a topic to•Pythagorean Theoremgo to thatsection•Distance Formula•Midpoints•GlossaryTeacherNotes3
Pythagorean TheoremClick to return tothe table of contents4
Pythagorean TheoremPythagorean theoremis used for right triangles. It was firstknown in ancient Babylon and Egypt beginning about 1900 B.C.However, it was not widely known until Pythagoras stated it.Pythagoras lived during the 6th century B.C. on the island ofSamos in the Aegean Sea. He also lived in Egypt, Babylon, andsouthern Italy. He was a philosopher and a teacher.5
Legs- Opposite the right angle- Longest of the 3 sides- 2 sides that form the right angleclick to revealcabHypotenuseclick to revealclick to revealLabelsfor aright triangle6
In a right triangle, the sum of the squares of thelengths of the legs (aandb) is equal to thesquare of the length of the hypotenuse (c).a2+ b2= c2Click on the linksbelow to see severalanimations of theproof•Water demo•Move slider to show c2•Moving of squaresPythagorean Theorem Proofs7
Proof of the Pythagorean TheoremLab: Proof of the Pythagorean TheoremTeacher'sNotes8
9Follow-up Questions:11.How is the area of the printed square on page 1 related to thearea of the printed square on page 2?Explain how you reachedthatconclusion.12.How are the 4 right triangles that you cut out at the beginningofMathPracticethis lab related to each other?Explain how you reachedthatconclusion.
10Follow-up Questions (cont'd):13.How are the areas that you found in question #6 & question#10 related to each other? Explain how you reached thatconclusion.14.What algebraic expression represents the side length of theMathPracticeprinted squares.Explain how you reached that conclusion.
11Follow-up Questions (cont'd):15.Multiply these side lengths together and simplify the expression.16.Using the arrangement of the shapes from question #5, write anMathPracticealgebraic expression to represent the area of the entire figure.
Follow-up Questions (cont'd):17.Set the expressions from question #15 & question #16 equal toone another and simplify the equation.MathPractice12
a2+ b2= c252+ b2= 15225 + b2= 225-25-25b2= 200MissingLegWriteEquationSubstitute in numbersSquare numbersSubtractFind the Square RootLabel Answer5 ft15 ftPythagorean Theorem13
9 in18 ina2+ b2= c292+ b2= 18281 + b2= 324-81-81b2= 243MissingLegWriteEquationSubstitute in numbersSquare numbersSubtractFind the Square RootLabel AnswerPythagorean Theorem14
MissingLegWriteEquationSubstitute in numbersSquare numbersSubtractFind the Square RootLabel AnswerMissingHypotenuseWriteEquationSubstitute in numbersSquare numbersAddFind the Square RootLabel Answer