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Unit 6: Scale Factor and Measurement

mariko-white avatar
mariko-white
10 diapositives · 267 Views · Oct 27, 2014

In this lesson, students will explore the relationship between similar plane figures using ratios and proportions. By learning to identify corresponding angles and sides, students will understand how to use proportions to find missing measurements in similar figures. We will also discuss the concepts of congruence and similarity, along with practical problem-solving techniques. Students will engage in exercises that reinforce their understanding of ratios, proportions, and the mathematical methods required to solve real-world measurement problems.

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Unit 6: Scale Factor and Measurement
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  1. Unit 6: Scale Factor and Measurement How will you measure up?

  2. Similar figures What am I Learning Today? How will I show that I learned it? Demonstrate the relationship between similar plane figures using ratio and proportion Use proportions to find missing measures in similar figures Solve problems using proportions

  3. Vocabulary • Corresponding: The relationship between the sides and angles of two or more objects that are matched • Similar: Figures with the same shape, but not necessarily the same size • Congruent: Figures that have the same size and shape

  4. Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

  5. What do you remember aboutRatio and Proportion? See if you can answer these… 1) What is a ratio? A comparison of two quantities measured in the same units 2) What is a proportion? An equation that shows two ratios are equivalent 3) Explain how you find a missing value in a proportion. Find the cross products. Isolate the variable using the inverse operation.

  6. Questions Notes = = L1 L2 L1 W1 W1 W2 L2 W2 Questions Answers How do I know two figures are similar? 1) The measure of the corresponding angles are equal 2) The ratios of the lengths of the corresponding sides are proportionate How can I find the length of a missing side of similar figures? 1) Write a proportion using corresponding sides 2) Use a tic-tac-toe grid to help set up the proportion correctly. 3) Solve proportion using cross product. What is a tic-tac-toe grid? or For example, ratios should be set up to compare length to length and width to width, which puts the first shape as both numerators and the second as both denominators. OR Ratios should compare a shape’s length to its width, which gives each shape its own ratio.

  7. Matching sides are • proportional • Matching angles have the • same measure. Figures that have the same shape, but may not be the same size. They also do not have to be in the same position. Similar Figures 6 3 8 15 9 5 3 3 3 4 3 12

  8. 52 5,200 50 50y ____ ___ _____ ___ 100 50 y 50 The two triangles are similar. Find the missing length y. A B 60 m 120 m 50 m 100 m 52 m y Write a proportion using corresponding side lengths. = 100 • 52= 50 •y The cross products are equal. y is multiplied by 50. 5,200= 50y Divide both sides by 50 to undo the multiplication. = y =104 meters

  9. 3 cm = w cm 162 2w 2 cm _____ ____ ___ 54 cm 2 2 This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting? Write a proportion. 54 • 3= 2 •w The cross products are equal. w is multiplied by 2. 162= 2w Divide both sides by 2 to undo the multiplication. = 81= w The width of the actual painting is 81 cm.

  10. Let’s Practice http://www.harcourtschool.com/activity/similar_congruent/ http://www.quia.com/rr/232263.html?AP_rand=243379547