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Happy Thursday!

Happy Thursday!. Take out your homework Take out notes from yesterday Tonight’s Homework Pg. 491 #1-6, 12- 14, 20- 23. Questions About Drawing?. Period 1: Extra Credit. Sub and Quiz on Monday. Chapter Test next Friday. I will give you a study guide on Wednesday

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Happy Thursday!

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  1. Happy Thursday! • Take out your homework • Take out notes from yesterday • Tonight’s Homework • Pg. 491 #1-6, 12-14, 20-23

  2. Questions About Drawing? Period 1: Extra Credit

  3. Sub and Quiz on Monday

  4. Chapter Test next Friday I will give you a study guide on Wednesday Study ALL of Chapter 7!

  5. 7.1-7.3 Quiz A: 25.5- 28 B: 22.5- 25 C: 19.5- 22 Below a 19 please come see me! You want to start off your second semester on the right track 

  6. Whiteboards Suppose that an artist decided to make a large sketch of trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in • Find LM • Find MN . • You can use a calculator if you wish

  7. Whiteboard After doing it on your whiteboard, copy it in your notes. On the map, 5th Ave., 6th Ave., and 7th Ave. are parallel. What is the length of Main St. between 5th Ave. and 6th Ave.?

  8. Whiteboards Find the length of each segment. 1.

  9. Whiteboards 3.Verify that BE and CD are parallel.

  10. 7.5: Using Proportional Relationships You will be able to: • Use ratios to make indirect measurements. • Use scale drawings to solve problems.

  11. 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.

  12. With your partner, discuss the following questions. • What appears to be true about the corresponding angles in the two triangles? • If the corresponding sides are proportional, what could you conclude about the triangles?

  13. 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.

  14. Indirect Measurement Indirect Measurement • Any method that uses formulas, similar figures, and/or proportions to measure an object. • 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.

  15. 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?

  16. Example 1: In reality, we are not all going to be measured to the nearest ft. For example, I am 5 foot 2 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?

  17. Example 1 Continued… Step 1 Convert the measurements to inches. Step 2: Find h.

  18. Whiteboard A student who is 5 ft 6 in. tall measured shadows to find the height LM of a flagpole. What is LM? 1. Convert to inches 2. Find h

  19. Scale Drawing • Represents an object as smaller than or larger than its actual size. The drawing’s scaleis the ratio of any length in the drawing to the corresponding actual length. • For example, on a map with a scale of 1 cm : 1500 m, one centimeter on the map represents 1500 m in actual distance.

  20. Example 2 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.

  21. Whiteboard Lady Liberty holds a tablet in her left hand. The tablet is 7.19 m long and 4.14 m wide. If you made a scale drawing using the scale 1 cm:0.75 m, what would be the dimensions to the nearest tenth?

  22. 3.7 in. 3 in. Example 3 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.

  23. 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?

  24. 7-5 Using Proportional Relationships Whiteboard • Take 2 minutes to write down your definition of perimeter and your definition of area. • Lets investigate what the relationship might be between the similarity ratio, perimeter, and area of a figure.

  25. 7-5 Using Proportional Relationships You will have the next 8 minutes to complete the Investigation.

  26. 7-5 Using Proportional Relationships

  27. 7-5 Using Proportional Relationships Example 3 Given that ∆LMN ~ ∆QRT, find the perimeter P and area A of ∆QRS.

  28. Whiteboards Example 3 (b) ∆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.

  29. Exit Ticket Create your own word problem and solve it that involves one of the following: • Indirect Measurement • Scale Drawing • Ratio of Area and Perimeter I may use this on your test!

  30. 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?

  31. Interactive Quiz! http://my.hrw.com/math06_07/nsmedia/practice_quizzes/geo/geo_pq_sim_04.html

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