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Transparency 6. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 6-2b. Objective. Determine whether figures are similar and find a missing length in a pair of similar figures. Example 6-2b. Vocabulary. Similar Figures.

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  1. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 6-2b Objective Determine whether figures are similar and find a missing length in a pair of similar figures

  4. Example 6-2b Vocabulary Similar Figures Figures that have the same shape but not necessarily the same size

  5. Example 6-2b Vocabulary Indirect measurement Finding a measurement by using similar triangles and writing a proportion

  6. Example 6-2b Vocabulary Proportion An equation that shows that two ratios are equivalent

  7. Example 6-2b Math Symbols Is similar to 

  8. Lesson 6 Contents Example 1Find Side Measures of Similar Triangles Example 2Use Indirect Measurement

  9. IfABC DEF, find the length of Example 6-1a Small = Large Triangles are similar so start with a proportion To set up determine what you are working with Small triangle and a large triangle 1/2

  10. IfABC DEF, find the length of Example 6-1a Small 3 = Large 4.5 Find a side on each triangle that is similar On the first ratio, put 3 with the small triangle On the first ratio, put 4.5 with the large triangle 1/2

  11. IfABC DEF, find the length of Example 6-1a Small 3 = x Large 4.5 Define the variable Since DF is on the large triangle, place the variable in the denominator Find the side similar to DF on the small triangle 1/2

  12. IfABC DEF, find the length of Example 6-1a Small 3 11 = x Large 4.5 Since 11 is with the small triangle, place 11 in the numerator Solve for x by using cross multiplication 1/2

  13. IfABC DEF, find the length of Example 6-1a Cross multiply Small 3 11 = Combine “like” terms x 4.5 Large Ask “What is being done to the variable?” 3x = 4.5(11) 3x = 49.5 The variable is being multiplied by 3 3 3 Do the inverse on both sides of the equal sign Using a fraction bar, divide both sides by 3 1/2

  14. IfABC DEF, find the length of Example 6-1a Combine “like” terms Small 3 11 = Use the Identity Property to multiply 1  x x 4.5 Large 3x = 4.5(11) The question asked to find the length of DF 3x = 49.5 3 3 Add dimensional analysis 1  x = 16.5 x = 16.5 Answer: DF = 16.5 cm 1/2

  15. IfJKL MNO, find the length of Example 6-1b Answer: JL = 13.5 in 1/2

  16. Example 6-2a A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? x ft 6 ft 9 ft 12 ft Draw a picture of the two windows and put in the dimensions Small = Large Set up the proportion Make the first ratio with similar sides from each window 2/2

  17. Example 6-2a A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? x ft 6 ft 9 ft 12 ft The small window length is 9 ft Small 9 x = The large window length is 12 ft Large 12 Define the variable The new window is the small window 2/2

  18. Example 6-2a A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? x ft 6 ft 9 ft 12 ft The similar wide is the width of the large window Small 9 x = Large 12 6 Find the value of x by cross multiplying 2/2

  19. Example 6-2a A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? Cross multiply x 9 Small = 6 Large 12 Combine “like” terms Ask “What is being done to the variable?” 12x = 9(6) 12x = 54 The variable is being multiplied by 12 12 12 Do the inverse on both sides of the equal sign Using a fraction bar, divide both sides by 12 2/2

  20. Example 6-2a A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? Combine “like” terms x 9 Small = 6 Large 12 Use the Identity Property to multiply 1  x 12x = 9(6) Add dimensional analysis 12x = 54 12 12 1  x = 4.5 Answer: x = 4.5 ft 2/2

  21. Example 6-2b * Tom has a rectangular garden which has a length of 12 feet and a width of 8 feet. He wishes to start a second garden which is similar to the first and will have a width of 6 feet. Find the length of the new garden. Draw the gardens and label dimensions Answer: x = 9 ft 2/2

  22. End of Lesson 6 Assignment

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