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Happy Monday! Take Out: Your Perspective Drawings HW #5 : Pg. 491 #1-6, 12-14, 20-23; p 508 #6 Updates: Unit 4 Part 1 Test ( 7.1-7.6 ) next week. I will tell you the date tomorrow! Remember: You can do quiz corrections if you come in during tutorial! ALSO, ask for help during tutorial! Agenda Perspective Drawings 7.5: Using Proportional Relationships Investigation! Quiz Master 7.1-7.3 Quiz You need to make it up TODAY or you will receive a ZERO! Perspective Drawings You may wonder how these drawings relate to Geometry? Take out a ruler. Measure lines that correspond to the same thing in your picture. Are the measurements proportional? 7.5: Using Proportional Relationships You will be able to: (1) Use ratios to make indirect measurements. (2) Use scale drawings to solve problems. Thales is known as the first Greek scientist, engineer, and mathematician. Legend says that he was the first to determine the height of the pyramids in Egypt! He did this by examining the shadows made by the Sun. He considered three points: the top of the pyramids, the lengths of the shadows, and the bases. With your table, discuss the following questions. (1) What appears to be true about the corresponding angles in the two triangles? (2) If the corresponding sides are proportional, what could you conclude about the triangles? Similarity is often used to measure heights and lengths of objects, build scale models, maps, and blueprints. Similarity is the one of the most useful applications of geometry. Indirect Measurement Indirect Measurement o Any method that uses formulas, similar figures, and/or proportions to measure an object. o Thales used indirect measurement to measure his height and the length of his shadow and compared it with the length of the shadow cast by the pyramid to find the height of the pyramid. 7-5 Using Proportional Relationships Whiteboards If Thales is 5ft tall, his shadow is 7 ft long, and the length of the pyramids shadow is 100 ft long, how tall is the pyramid? Example 1: In reality, we are not all going to be measured to the nearest ft. For example, I am 5 foot 3 inches. Tyler wants to find the height of a telephone pole. He measured the poles shadow and his own shadow and then made a diagram. What is the height h of the pole? Example 1(a) Continued… Step 1 Divide inches/12 to see how much of a foot that is. Step 2: Find h. Example 1(b) Drop Zone in Great America casts a shadow that is 43⅔ ft long. At the same time, a 6 ft 4 in. tall person standing in line casts a shadow 2 ft long. What is the height of the ride? Round to the nearest tenth. Whiteboard A student who is 5 ft 6 in. tall measured shadows to find the height LM of a flagpole. What is LM? Scale Drawing 0 Represents an object as smaller than or larger than its actual size. The drawing’s scale is the ratio of any length in the drawing to the corresponding actual length. 0 For example, you did a scale on your Chapter 7 project. You showed how many cm/inches your bed was on your picture to the actual length of your bed. Example 2(a) Rachel is a cartographer. She is currently making a map of Australia. She wants to make her map scale 1-inch for every 200 km. Australia is 4000 km wide. If her paper is 11 inches wide, can she fit a drawing of the whole continent onto the paper? Justify your response. Example 2(b) An artist makes a scale drawing of a new lion enclosure at the San Francisco Zoo. The scale is 1 in : 25 ft. On the drawing, the length of the enclosure is 7 ¼ inches. What is the actual length of the lion enclosure? Round to the hundredth. Example 2( c) The rectangular central chamber of the Lincoln Memorial is 74 ft long and 60 ft wide. Make a scale drawing of the floor of the chamber using a scale of 1 in.:20 ft. 3.7 in. 3 in. Math Joke of the Day! Q: How many seconds are there in a year? A: Twelve. January second, February second, March second… 7-5 Using Proportional Relationships We have discussed a lot about similar triangles and their side lengths. What about similar triangles and their perimeters? What about similar triangles and their areas? 7-5 Using Proportional Relationships Whiteboard o Take 2 minutes to write down your definition of perimeter and your definition of area. o Lets investigate what the relationship might be between the similarity ratio, perimeter, and area of a figure. 7-5 Using Proportional Relationships You will have the next 8 minutes to complete the Investigation on the back of your notes. 7-5 Using Proportional Relationships 7-5 Using Proportional Relationships Example 3 Given that ∆LMN ~ ∆QRT, find the perimeter P and area A of ∆QRS. Whiteboards ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A = 96 mm2 for ∆DEF, find the perimeter and area of ∆ABC. Quiz Master Create your own word problem and solve it that involves one of the following: o Indirect Measurement o Scale Drawing o Ratio of Area and Perimeter I may use this on your test! Exit Ticket 1Maria is 4 ft 2 in. tall. To find the height of a flagpole, she measured her shadow and the pole’s shadow. What is the height h of the flagpole? 2. A blueprint for Latisha’s bedroom uses a scale of 1 in.:4 ft. Her bedroom on the blueprint is 3 in. long. How long is the actual room? Interactive Quiz! http://my.hrw.com/math06_07/nsmedia/practice_quizzes/geo /geo_pq_sim_04.html