Lesson 9.1 • The Theorem of Pythagoras

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Lesson 9.6 • Circles and the Pythagorean Theorem Name Period Date In Exercises 1 and 2, find the area of the shaded region in each figure. All measurements are in centimeters. Write your answers in terms of and rounded to the nearest 0.1 cm 2 . 1. AO 5. AC 8. 2. Tangent PT , QM12, mP 30° A 3. AP 63 cm. Radius of circle O 37 cm. How far is A from the circumference of the circle? 4. Two perpendicular chords with lengths 12.2 cm and 8.8 cm have a common endpoint. What is the area of the circle? 5. ABCD is inscribed in a circle. AC is a diameter. If AB 9.6 cm, BC 5.7 cm, and CD 3.1 cm, find AD. 6. Find ST. 7. The coordinate of point M is 3 , 2 1 2 . Find the measure of AOM. 6 O C O S 30° R B T P 3 P M O S P (0, 1) O y T M A A x (1, 0) 64 CHAPTER 9 Discovering Geometry Practice Your Skills Q ©2008 Kendall Hunt Publishing
4. It is too late to change the area. The length of the diagonals determines the area. LESSON 8.4 • Areas of Regular Polygons 1. A 696 cm 2 2. a 7.8 cm 3. p 43.6 cm 4. n 10 5. s 4 cm, a 2.8 cm, A 28 cm 2 6. Possible answer (s will vary): s 3.1 cm, a 3.7 cm, A 45.9 cm 2 7. Approximately 31.5 cm2 : area of square 36; area of square within angle 3 8 36 13.5; area of octagon 120; area of octagon within angle 3 8 120 45; shaded area 45 13.5 31.5 cm2 LESSON 8.5 • Areas of Circles 1. 81 cm 2 2. 10.24 cm 2 3. 23 cm 4. 324 cm 2 5. 191.13 cm 2 6. 41.41 cm 7. 7.65 cm 2 8. 4.90 cm 2 9. 51.3 cm 2 10. 33.5 or 33.6 cm 2 11. (64 128) square units 12. 25 cm 2 LESSON 8.6 • Any Way You Slice It 1. 25 12 cm2 6.54 cm2 2. 32 3 cm2 33.51 cm2 3. 12 cm2 37.70 cm2 4. (16 32) cm 2 18.27 cm 2 5. 13.5 cm 2 42.41 cm 2 6. 10 cm 2 31.42 cm 2 7. r 10 cm 8. x 135° 9. r 7 cm LESSON 8.7 • Surface Area 1. 136 cm 2 2. 240 cm 2 3. 558.1 cm 2 4. 796.4 cm 2 5. 255.6 cm 2 6. 356 cm 2 7. 468 cm 2 8. 1055.6 cm 2 9. 1 sheet: front rectangle: 3 1 1 2 41 ; 2 back rectangle: 3 2 1 2 71 2 ; bottom rectangle: 3 2 6; side trapezoids: 22 8; total 26 ft2 2 . Area of 1 sheet 4 8 32 ft 2 . Possible pattern: LESSON 9.1 • The Theorem of Pythagoras 1. a 21 cm 2. p 23.9 cm 3. x 8 ft 4. h 14.3 in. 5. Area 19.0 ft 2 6. C(11, 1); r 5 7. Area 49.7 cm 2 8. RV 15.4 cm 9. If the base area is 16 cm 2 , then the radius is 4 cm. The radius is a leg of the right triangle; the slant height is the hypotenuse. The leg cannot be longer than the hypotenuse. 10. Area 150 in 2 ; hypotenuse QR 25 in.; altitude to the hypotenuse 12 in. LESSON 9.2 • The Converse of the Pythagorean Theorem 1. No 2. Yes 3. Yes 4. Yes 5. Area 21.22 cm 2 6. The top triangle is equilateral, so half its side length is 2.5. A triangle with sides 2.5, 6, and 6.5 is a right triangle because 2.5 2 6 2 6.5 2 . So, the angle marked 95° should be 90°. 7. x 44.45 cm. By the Converse of the Pythagorean Theorem, ADC is a right triangle, and ADC is a right angle. ADC and BDC are supplementary, so BDC is also a right triangle. Use the Pythagorean Theorem to find x. Discovering Geometry Practice Your Skills ANSWERS 109 ©2008 Kendall Hunt Publishing 1_ 1 2 ft 1_ 2 2 ft Side Side 2 ft 1_ 2 2 ft 1_ 1 2 ft 2 1 2 1 1 2 Front Back 1_ 1 2 ft 1_ 2 2 ft 2 ft Left over 3 ft Bottom 3 ft 3 ft 2 ft
Page 1 and 2: Lesson 9.1 • The Theorem of Pytha
Page 3 and 4: Lesson 9.3 • Two Special Right Tr
Page 5: Lesson 9.5 • Distance in Coordina
Page 9: LESSON 9.6 • Circles and the Pyth

Lesson 9.1 • The Theorem of Pythagoras

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