Angle Relationships in Parallel Lines and Triangles
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1 ? UNIT 5 Study Guide Review MODULE ESSENTIL QUESTION ngle Relationships in Parallel Lines and Triangles How can you solve real-world problems that involve angle relationships in parallel lines and triangles? EXMPLE Find each angle measure when m 6 = 8. m 5 m 5 = 80-8 = 99 5 and 6 are supplementary angles. m m = 99 m l t Key Vocabulary alternate exterior angles (ángulos alternos externos) alternate interior angles (ángulos alternos internos) corresponding angles (ángulos correspondientes (para líneas)) exterior angle (ángulo externo) interior angle (ángulos internos) remote interior angle (ángulo interno remoto) same-side interior angles (ángulos internos del mismo lado) similar (semejantes) transversal (transversal) and 5 are corresponding angles. m 3 m 3 = 80-8 = 99 3 and 6 are same-side interior angles. EXMPLE 2 re the triangles similar? Explain your answer. y = 80 - ( ) y = 78 x = 80 - ( ) x = 46 The triangles are not similar, because they do not have 2 or more pairs of corresponding congruent angles E x y D F 42
2 EXERISES. If m GH = 06, find the measures of the given angles. (Lesson.) E G D m EG = m EGD = H F m HF = m HGD = 2. Find the missing angle measures. (Lesson.2) L 25 m JKL = J K 40 M m LKM = 3. Is the larger triangle similar to the smaller triangle? Explain your answer. (Lesson.3) x cm y cm 3 cm 5 cm 4. Find the value of x and y in the figure. (Lesson.3) 0 cm 4 cm 5. If m JI = 32 and m EIH = 59, find the measures of the given angles. (Lesson.) E I H m IKJ = m HI = G J F K D m EIJ = m IK = 422
3 ? MODULE 2 ESSENTIL QUESTION The Pythagorean Theorem How can you use the Pythagorean Theorem to solve real-world problems? Key Vocabulary hypotenuse (hipotenusa) legs (catetos) Pythagorean Theorem (teorema de Pitágoras) EXMPLE Find the missing side length. Round your answer to the nearest tenth. b 7 in. 8 in. a 2 + b 2 = c b 2 = b 2 = 324 b 2 = 275 b = _ The length of the leg is about 6.6 inches. EXMPLE 2 Thomas drew a diagram to represent the location of his house, the school, and his friend Manuel s house. What is the distance from the school to Manuel s house? Round your answer to the nearest tenth. Manuel s house a 2 + b 2 = c = c = c 2 9 mi c 2 = 06 c = _ School 5 mi Thomas s house The distance from the school to Manuel s house is about 0.3 miles. EXERISES Find the missing side lengths. Round your answers to the nearest hundredth. (Lesson 2.) ft 0 ft s r l = 25 cm h = 0 cm w = 0 cm 423
4 3. Hye Sun has a modern coffee table whose top is a triangle with the following side lengths: 8 feet, 3 feet, and 5 feet. Is Hye Sun s coffee table top a right triangle? (Lesson 2.2) 4. Find the length of each side of triangle. If necessary, round your answers to the nearest hundredth. (Lesson 2.3) _ y O x? MODULE 3 ESSENTIL QUESTION Volume How can you solve real-world problems that involve volume? Key Vocabulary cone (cono) cylinder (cilindro) sphere (esfera) EXMPLE Find the volume of the cistern. Round your answer to the nearest hundredth. Use 3.4 for π. 5 ft V = πr 2 h ft 47.9 The cistern has a volume of approximately 47.9 cubic feet. EXMPLE 2 Find the volume of a sphere with a radius of 3.7 cm. Write your answer in terms of π and to the nearest hundredth. V = 4_ 3 πr 3 V = 4_ 3 πr 3 4_ 3 π _ 3 π π 4_ _ The volume of the sphere is approximately 67.54π cm 3, or cm
5 EXERISES Find the volume of each figure. Round your answers to the nearest hundredth. Use 3.4 for π. (Lessons 3., 3.2, 3.3). 2 mm 2. 4 mm 34 in. 50 in cm 2.2 m.4 m in..2 in. 0 yd 3.3 yd 7. Find the volume of a ball with a radius of.68 inches. 8. round above-ground swimming pool has a diameter of 5 ft and a height of 4.5 ft. What is the volume of the swimming pool? 9. paper cup in the shape of a cone has a height of 4.7 inches and a diameter of 3.6 inches. What is the volume of the paper cup? 425
6 Unit Project 8.G.7 The Wheel of Theodorus The Wheel of Theodorus is named after Theodorus of yrene, who lived at the time of Pythagoras of the Pythagorean theorem. For this project you will draw and decorate a Wheel of Theodorus. You ll need a large piece of paper, a right angle, and a ruler. egin with a right triangle that has both legs unit long. Next, draw a second right triangle so that the hypotenuse of the first triangle is one of the legs of the second triangle and the other leg is unit long, as shown in the diagram. Draw a third right triangle beginning with the hypotenuse of the second triangle as one leg of the third triangle and a -unit leg as the other leg. ontinue drawing right triangles in this manner until you have 6 triangles. Decorate your Wheel of Theodorus. alculate the lengths of the hypotenuses of the 6 triangles. Write a brief report on Theodorus of yrene. Use the space below to write down any questions you have or important information from your teacher. This Wheel of Theodorus shows the first four triangles. MTH IN REERS TIVITY Hydrologist hydrologist needs to determine if an underground aquifer, which is roughly cylindrical in shape, is totally filled with water. The diameter of the aquifer is 70 meters, and its depth is 9 meters. The mass of the water in it is kilograms. One cubic meter of water has a mass of about 000 kilograms. Is the aquifer totally filled with water? Explain how you determined your answer. 426
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