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

3. Splash Screen

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

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

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

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

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

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

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

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

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

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

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

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

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

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? Draw a picture of the two windows and put in the dimensions 2/2 12 ft 6 ft 9 ft x ft Set up the proportion Small Large = Make the first ratio with similar sides from each window

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? The small window length is 9 ft 2/2 12 ft 6 ft 9 ft x ft Small Large = 9 The large window length is 12 ft 12 Define the variable The new window is the small window x

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? The similar wide is the width of the large window 2/2 12 ft 6 ft 9 ft x ft Small Large = 9 12 x 6 Find the value of x by cross multiplying

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? 2/2 Small Large = 9 12 x 6 Cross multiply 12x = 9(6) Combine “like” terms 12x = 54 Ask “What is being done to the variable?” The variable is being multiplied by 12 Do the inverse on both sides of the equal sign Using a fraction bar, divide both sides by 12 12

21. 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? 2/2 Small Large = 9 12 x 6 12x = 9(6) 12x = 54 12 Combine “like” terms 1  x = 4.5 Use the Identity Property to multiply 1  x x = 4.5 Add dimensional analysis ft Answer:

22. 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

23. End of Lesson 6 Assignment Lesson 10:6Similar Figures3 - 12 All