Ext 6-8 Sampler

PythagoreanTheorem 56 Grade8 PartB Lesson28, 8ETeacherGuide 80 Objective56: Touse thePythagoreanTheorem to find the missing sideof a right triangle. Materials: InchGraphPaper (Master 4),CentimeterGraph Paper (Master 8), scissors, tape MissingSide of aRight Triangle Review the activitydoneonpage79. Each small group will need2 sheets of InchGraphPaper (Master 4) and scissors.Outline and cut out right triangleswith legs of 3" and4" and ahypotenuseof 5". Cut out 3 squareshaving one side the same as each sideof the right triangle. What is the special relationship involving the squareson the sides of a right triangle? (The sumof the squares of the two smaller sides equals the squareof the longest side.) This special relationship is called thePythagoreanTheorem. Anotherwayof showing this special relationship is a 2 + b 2 = c 2 . Cover the squareof 5with another sheet of paper and ask, If youknow that the lengthsof the two legsof a right triangleare3and4, how couldyou find the lengthof the hypotenuse? (Add the squares of the two legs. Find the square root of the sum.) Record this algebraically: 3 2 +4 2 = c 2 9+16= c 2 25= c 2 √25= c 5= c Now cover the squareof 4with a sheet of paper. If you know that one leg is3and thehypotenuse is5, howwould you find the lengthof themissing leg? (Subtract the squareof the leg from the squareof thehypotenuse. Find the square root of thedifference.) Record this algebraically: 3 2 + b 2 =5 2 9+ b 2 =25 b 2 =16 b =√16 b =4 PythagoreanTheoremPractice Each small groupof studentswill need2 sheets of CentimeterGraphPaper and a cut out right trianglewith legs of 5 cm and12 cm. Have students cut out a5 cm 5 cm square and a 12 cm 12 cm square fromone sheet of their graphpaper, and tape these squares on the corresponding legs of their triangle. What is the lengthof thehypotenuse?How can we find the lengthof amissing sideof a triangle? (use the PythagoreanTheorem). Record the solutionprocess on the board (hypotenuse=13 cm), thenhave students cut out a 13 cm 13 cm square from their secondpieceof graph paper and tape it on thehypotenuseof their triangle. Read the illustration together. Emphasize that the letters a and b will always refer to the legs and the letter c to the hypotenuse. Ask student volunteers todescribe in their ownwords themeaning associatedwith a 2 + b 2 = c 2 . (In a right triangle, the squareof leg a added to the squareof leg b equals the squareof thehypotenuse c .) Skill Builders 56-1, 56-3 Part B 80 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Using the PythagoreanTheoremTo Find aMissingSide The PythagoreanTheorem: The sum of the squares of the legs is equal to the square of the hypotenuse. leg a hypotenuse c leg b leg a squared + leg b squared equals hypotenuse c squared Wewrite: a 2 + b 2 = c 2 You can use the PythagoreanTheorem to find themissing side of any right triangle. 5 12 hypotenuse = ? a 2 + b 2 = c 2 5 2 + 12 2 = c 2 25 +144 = c 2 169 = c 2 If c 2 = 169, c = √169 c = 13 1. c 2 = 25, c =___ 2. c 2 =100, c =___ 3. c 2 = 625, c =___ 4. c 2 = 49, c =___ Find the hypotenuse ormissing leg. Use the PythagoreanTheorem. 5. ____ + ____ = _____ c 2 = _____ c = _____ 6. ____ + ____ = _____ c 2 = _____ c = _____ 7. ____ + ____ = _____ c 2 = _____ c = _____ 4 3 c = ? 8 15 c = ? 6 8 c = ? 8. ____ + ____ = _____ b 2 = _____ b = _____ 9. ____ + ____ = _____ a 2 = _____ a = _____ 10. ____ + ____ = _____ b 2 = _____ b = _____ 10 6 b = ? 15 12 a = ? 24 25 b = ? A telephone pole is 30 feet tall. A stabilizing cablewill run from the top of the pole to a point 40 ft. away. How longwill the cable be?Show your work and explain inwords. 30 ft. 40 ft. ? 5 10 25 7 3 2 6 2 8 2 a 2 6 2 24 2 4 2 b 2 15 2 12 2 8 2 b 2 c 2 10 2 c 2 15 2 c 2 25 2 25 64 289 81 100 49 5 8 The cablewill be50 ft. long. c 2 =30 2 +40 2 c 2 =900+ 1600 c 2 =2500 c =50 17 9 10 7 8.G.7