Three squares with sides 3, 4, and 5 units are used to form the right triangle shown. In a right triangle, the sides have special names.

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1 1- The Pythgoren Theorem MAIN IDEA Find length using the Pythgoren Theorem. New Voulry leg hypotenuse Pythgoren Theorem Mth Online glenoe.om Extr Exmples Personl Tutor Self-Chek Quiz Three squres with sides 3, 4, nd 5 units re used to form the right tringle shown. 3 units 1. Find the re of eh squre.. How re the squres of the sides relted to the res of the squres? 3. Find the sum of the res of the two smller squres. How does the sum ompre to the re of the lrger squre? 4. Use grid pper to ut out three squres 4 units with sides 5, 1, nd 13 units. Form right tringle with these squres. Compre the sum of the res of the two smller squres with the re of the lrger squre. 5 units In right tringle, the sides hve speil nmes. The two sides tht form the right ngle re the legs. The side opposite the right ngle is the hypotenuse. It is the longest side of the tringle. The Pythgoren Theorem desries the reltionship etween the length of the hypotenuse nd the lengths of the legs. Pythgoren Theorem Key Conept Words In right tringle, the squre of the length of the hypotenuse equls the sum of the squres of the lengths of the legs. Model Symols = + When using the Pythgoren Theorem, you will enounter equtions tht involve squre roots. Every positive numer hs oth positive nd negtive squre root. By the definition of squre roots, if n =, then n = ±. The nottion ± indites oth the positive nd negtive squre root of numer. You n use this reltionship to solve equtions tht involve squres. 640 Chpter 1 Geometry nd Mesurement

2 Find the Length of the Hypotenuse 1 Find the length of the hypotenuse of the tringle. = + =8 +4 Pythgoren Theorem Reple with 8 nd with 4. = Evlute 8 nd 4. = 80 Add. = ± 80 Definition of squre root ± 8.9 Simplify. 8 ft ft 4 ft The length of the hypotenuse is out 8.9 feet.. Find the length of the hypotenuse of right tringle with legs 5 yrds nd 7 yrds. Round to the nerest tenth. SCUBA DIVING A su diver dove 14 feet elow the surfe. Then, he swm 16 feet towrd orl formtion. How fr is the diver from his ot? The diver s distne from the ot is the hypotenuse of right tringle. Write nd solve n eqution for x. = + x = Pythgoren Theorem Reple with x, with 14, nd with 16. x = Evlute 14 nd 16. x = 45 Add. x = ± 45 Definition of squre root x ±1.3 Simplify. The diver s distne from the ot is out 1.3 feet. nd se 60 ft mesuring 60 feet on eh side. How fr does plyer on seond se throw when she throws from seond se to home? Round to the nerest tenth. ft. SOFTBALL A softll dimond is squre 60 Chek for Resonleness You n eliminte -8.9 s solution euse the length of side of tringle nnot e negtive numer. home Lesson 1- The Pythgoren Theorem 641

3 You n lso use the Pythgoren Theorem to find the mesure of leg if the mesure of the other leg nd the hypotenuse re known. Find the Length of Leg 3 Find the missing mesure of the tringle. 13 m Round to the nerest tenth if neessry. The missing mesure is the length of leg. = + Pythgoren Theorem 13 = 5 + Reple with 5 nd with = 5 + Evlute 13 nd = - 5 Sutrt 5 from eh side. 144 = Simplify. ± 144 = Definition of squre root 1 = Simplify. The length of the leg is 1 entimeters. m 5 m. ft 17 ft d. 9. m 4 m m e. = 7 in., = 5 in. 4 in. 8 ft 15 ft 8.3 m Formuls Some formuls will e given to you during the test. It is good ide to fmilirize yourself with the formuls efore the test. 4 Mr. Thomson reted mosi tile in the shpe of squre to ple in his kithen. 9 in. 9 in. Whih is losest to the length of the digonl of the tile? A 10 in. C 15 in. B 13 in. D 17 in. Red the Item You need to use the Pythgoren Theorem to find the length of the digonl. 64 Chpter 1 Geometry nd Mesurement

4 Solve the Item = + Pythgoren Theorem = Reple with 9 nd with 9. = Evlute 9 nd 9. = 16 Add. = ± 16 Definition of squre root ±1.7 Simplify. The length is out 1.7 inhes. The nswer hoie losest to 1.7 inhes is 13 inhes. So, the nswer is B. f. A pinter lens ldder ginst the side of uilding. How fr from the ottom of the uilding is the top of the ldder? F F 38. ft H 1.8 ft G 8.0 ft J 0.0 ft 40 ft 1 ft indites multi-step prolem Exmples 1, 3 (pp ) Find the missing mesure of eh tringle. Round to the nerest tenth if neessry. 1. mm 6 mm 4 mm 10 mm. 19 in. 4.5 in. 31 in. in. 3. = 1 m, = 8 m 4. = 11 yd, = 1 yd m yd Exmple (p. 641) 5. ARCHITECTURE Wht is the width of the the fene gte shown t the right? Round to the nerest tenth. 4.0 ft.5 ft 4.7 ft Exmple 4 (pp ) 6. MULTIPLE CHOICE A ompny designed puli ply re in the shpe of squre. The ply re will inlude pthwy, s shown. Whih is losest to the length of the pthwy? C 100 yd A 100 yd B 15 yd C 140 yd D 175 yd 100 yd Lesson 1- The Pythgoren Theorem 643

5 HOMEWORK For Exerises 7 8, 11 1, , HELP See Exmples Find the missing mesure of eh tringle. Round to the nerest tenth if neessry in. 8. m 8m 9. 5m 1 in. 8 in. m 14 m m 4 15 m 1. m 4.6 ft ft mm 8.9 mm 11.5 m 8.9 mm.8 ft 13. =.4 yd, = 3.7 yd 14. = 8.5 m, = 10.4 m 15. = 7 in., = 4 in. 16. = 13.5 mm, = 18 mm MEASUREMENT For Exerises 17 nd 18, find eh distne to the nerest tenth mi shool nk 4.6 mi x mi 14.5 ft x ft 1.8 ft store SPORTS For Exerises 19 nd 0, find the length or width of eh piee of sports equipment. Round to the nerest tenth x in in. in in. in. x in. 1. MEASUREMENT A rn door is 10 feet wide nd 15 feet tll. A squre plnk 16 feet on eh side must e tken through the doorwy. Cn the plnk fit through the doorwy? Justify your nswer. 15 ft. MEASUREMENT On weekend trip round Cliforni, EXTRA PRACTICE See pges 70, Sydney left her home in Modesto nd drove 75 miles est to Yosemite Ntionl Prk, then 70 miles south to Fresno, nd finlly 110 miles west to Monterey By. Aout how fr is she from her strting point? Justify your nswer with drwing. Chpter 1 Geometry nd Mesurement 10 ft

6 H.O.T. Prolems 3. CHALLENGE Wht is the length of the digonl shown in the ue t the right? x in. 6 in. 4. FIND THE ERROR Mrus nd Aish re writing n eqution to find the missing mesure of the tringle t the right. Who is orret? Explin. 8 m 1 m x m 1 = 8 + x x = WRITING IN Mrus Aish 5. MATH Write prolem out rel-world sitution in whih you would use the Pythgoren Theorem. 6. Whih tringle hs sides,, nd so tht the reltionship + = is true? A B C D 7. An isoseles right tringle hs legs tht re eh 8 inhes long. Aout how long is the hypotenuse? F 1.8 inhes G 11.3 inhes H 8 inhes J 4 inhes 8. ESTIMATION Whih is loser to 55 : 7 or 8? (Lesson 1-1) 9. MEASUREMENT A ylinder-shped poporn tin hs height of 1.5 feet nd dimeter of 10 inhes. Find the volume to the nerest ui inh. (Lesson 11-10) Write eh perent s deiml. (Lesson 4-7) % 31. 8% 3. 14% % 34. PREREQUISITE SKILL The verge person tkes out 15 reths per minute. At this rte, how mny reths does the verge person tke in one week? Use the solve simpler prolem strtegy. (Lesson 11-5) Lesson 1- The Pythgoren Theorem 645

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