2. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

3. Splash Screen

4. Example 7-2c Objective Solve problems involving similar triangles

5. Example 7-2c Vocabulary Indirect measurement A technique using proportions to find a measurement

6. Lesson 7 Contents Example 1Use Shadow Reckoning Example 2Use Indirect Measurement

7. Example 7-1a TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 1/2 Write a ratio of the shadows A tree in front of Marcel’s house has a shadow 12 feet long Tree12 feet Marcel Marcel has a shadow 3 feet long 3 feet Write a ratio of the actual size of Marcel and the tree Tree Marcel h feet Define the variable Marcel is 5.5 feet 5.5 feet

8. Example 7-1a TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 1/2 Tree12 feet Marcel3 feet Tree Marcel h feet 5.5 feet Write a proportion using the 2 ratios 12 feet 3 feet = h feet 5.5 feet Cross multiply 3h3h =3h = 12(5.5)

9. Example 7-1a TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 1/2 Bring down 3h = 12 feet 3 feet = h feet 5.5 feet 3h = 12(5.5) 3h = Multiply 12  5.5 3h = 66 Ask “what is being done to the variable?” The variable is being multiplied by 3 Do the inverse operation on both sides of the equal sign

10. Example 7-1a TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 1/2 Bring down 3h = 66 12 feet 3 feet = h feet 5.5 feet 3h = 12(5.5) 3h =3h = 66 Using the fraction bar, divide both sides by 3 3 3 Combine “like” terms 1  h Bring down = 1  h = Combine “like” terms 1  h = 22

11. Example 7-1a TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 1/2 Use the Identify Property to multiply 1  h 3h = 66 3 3 1  h = 22 h Bring down = 22 h = 22 Add dimensional analysis h = 22 feet Answer: The tree is 22 feet tall.

12. Example 7-1c Jayson casts a shadow that is 10 feet. At the same time, a flagpole casts a shadow that is 40 feet. If the flagpole is 20 feet tall, how tall is Jayson? Answer: 5 feet 1/2

13. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 The prompt states the triangles are similar so can write ratios Write a ratio of similar sides  C is congruent on both triangles and the right angles are congruent from  C

14. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 CD is similar to CB so write a ratio using their lengths Large triangle60 m Small triangle20 m AB is similar to DE so write the 2 nd ratio Large triangle Small triangle 48 m d m Write a proportion using the 2 ratios 60 m 20 m = 48 m d m

15. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 60 m 20 m = 48 m d m Cross multiply the numbers 60d 60d =60d = 20(48) Bring down 60d = 60d = Multiply 20  48 60d = 960 Ask “what is being done by the variable”? The variable is being multiplied by 60

16. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 60 m 20 m = 48 m d m Do the inverse on both sides of the equal sign 60d 60d =60d = 20(48) 60d = 60d = 960 Bring down 60d = 960 60d = 960 Using the fraction bar, divide both sides by 60 60

17. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 Combine “like” terms 60d = 960 60 1  d Bring down = 1  d = Combine “like” terms 1  d = 16 Use the Identify property to multiply 1  d d Bring down = 16 d = 16

18. Example 7-2a SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 2/2 Add dimensional analysis 60d = 960 60 1  d1  d =1  d = 16 d d = 16d = 16 m Answer: The distance across the stream is 16 meters.

19. Example 7-2c SURVEYING The two triangles shown in the figure are similar. Find the distance d across the river. Answer: 7 feet * 2/2

20. End of Lesson 7 Lesson 4:7Indirect Measurement3 - 13 All Assignment