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© Glencoe/McGraw-Hill NAME 6–5 DATE PERIOD 6–6 Enrichment NAME DATE Traceable Figures The Pythagorean Theorem Try to trace over each of the figures below without tracing the same segment twice. In a right triangle, the square of the hypotenuse, c, is equal to the sum of the squares of the lengths of the other two sides, a and b. B A K J P PERIOD Study Guide c2 52 52 25 L Q a2 ! b2 32 ! 42 9 ! 16 25 M C Example: How long must a ladder be to reach a window 13 feet above ground? For the sake of stability, the ladder must be placed 5 feet away from the base of the wall. The figure at the left cannot be traced, but the one at the right can. The rule is that a figure is traceable if it has no points, or exactly two points where an odd number of segments meet. The figure at the left has three segments meeting at each of the four corners. However, the figure at the right has exactly two points, L and Q, where an odd number of segments meet. A14 yes, E D 5 2. E P 3 A 2. How long must the brace be on a closet rod holder if the vertical side is 17 cm and the horizontal side must be attached 30 cm from the wall? 84.9 ft V B Geometry: Concepts and Applications 2 3. S 6 E F yes, X W 8 9 X 5 3 4 Y 10 4. A © Glencoe/McGraw-Hill B yes, D C 7 3 12 8 3. If Briny is 32 miles due east of Oxford and Myers is 21 miles due south of Oxford, how far is the shortest distance from Myers to Briny? 4. In a baseball game, how far must the shortstop (halfway between second base and third base) throw to make an out at first base? 100.6 ft 2 1 D 11 2 1 11 34.5 cm R 13 H 1. In a softball game, how far must the catcher throw to second base? no U C 4 1 7 Solve. Round decimal answers to the nearest tenth. T 6 (13)2 ! (5)2 169 ! 25 194 w9 w4 w or about 13.9 ft Ï1 G E 9 10 H F 6 5 K 4 38.3 mi J G 247 Geometry: Concepts and Applications © Glencoe/McGraw-Hill 248 Geometry: Concepts and Applications (Lessons 6-5 and 6-6) c2 c2 c2 c2 Determine whether each figure can be traced. If it can, then name the starting point and number the sides in the order in which they should be traced. Sample answers are given. 1. Answers D © Glencoe/McGraw-Hill NAME 6–6 DATE PERIOD Skills Practice Find the missing measure in each right triangle. Round to the nearest tenth, if necessary. 2. PERIOD If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. 3. c in. 10 in. 4 cm DATE Practice The Pythagorean Theorem The Pythagorean Theorem 1. NAME 6–6 33 ft 20 ft c cm 1. a 8, b 13, c 3. a Ï1 w3 w,w b ? 15.3 2. a 4, c 6, b 4. b Ï5 w2 w, c ? 4.5 25 in. b ft 3 cm 5 4. 26.9 26.2 5. 8 in. b in. 9 in. 28 m am ? 5 Ï1 w0 w1 w, a ? 7 Find the missing measure in each right triangle. Round to the nearest tenth, if necessary. am 6. Ï1 w2 w, c 5. 5 6. 10.6 7. 7.2 8. 17.9 9. 7.5 10. 2.8 11. 34 12. 25 3m 4.5 m 4.1 26.2 7. 8. 3.4 9. 25 m 24 ft 6 ft c in. 3 in. am A15 b ft 29 m Answers 10 m 5 in. 14.7 23.2 Find each missing measure if c is the measure of the hypotenuse. Round to the nearest tenth, if necessary. 11. b 6, c 10, a ? 8 10. a 15, b 10, c ? 18.0 Geometry: Concepts and Applications 12. c 100, b 14. a 2, b 3, c 60, a 16. b 7, c 15, a ? 80 3.6 ? 13.3 ? 13. c 16, a 15. c 5, b 17. c 30, a 9, b 2, a 20, b 13.2 ? 4.6 ? 22.4 ? The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 18. 3 cm, 4 cm, 5 cm yes 19. 1 ft, 1 ft, 2 ft no 20. 2 in., 2 in., 4 in. no 22. 5 in., 10 in., 15 in. 21. 8 m, 15 m, 17 m no yes 23. 14 cm, 48 cm, 50 cm yes The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 13. 14 ft, 48 ft, 50 ft yes 15. 15 cm, 36 cm, 39 cm © Glencoe/McGraw-Hill 249 Geometry: Concepts and Applications © Glencoe/McGraw-Hill 14. 50 yd, 75 yd, 85 yd yes no 16. 45 mm, 60 mm, 80 mm 250 no Geometry: Concepts and Applications (Lesson 6-6) 5.8