1. Similar Triangles and Problem Solving
Lesson 13.5
Similar Triangles and Problem Solving pp

2. Objectives:
1. To apply the proportions from similar triangles to solve word problems.
2. To apply scale proportions to compute mileage or distances on a scale drawing or map.

3. EXAMPLE 1 Suppose that you are standing in front of the capitol in Washington, D.C., and that you want to know the building’s height above the street level but cannot measure it directly. How can you find the height of the building?

4. EXAMPLE 1 E 6
345 5 DE =
ABC ~ DBE C 5 B A D 6
345

5. EXAMPLE 2 A state park is building a boardwalk trail for visitors through a wetland. The plan calls for the trail to cross part of the pond as it winds through the surrounding marsh and bog. How long must the bridge be to cross the pond at the points indicated?

6. EXAMPLE 2 DC BC ED AB = 10 60 12 AB = 10(AB) = (60)(12) 10AB = 720
AB = 72 feet

7. Practice: If a vertical yardstick casts a 5-foot shadow, how high is a building that casts a 170-foot shadow?
170 5 x 3 = x
170 5

8. Practice: Scott’s dog Rusty is two feet high and casts a 15-inch shadow. How long is Scott’s shadow if he is 5’11”? x 15 71 24 =

9. Practice: The scale on a map shows one inch = 60 feet
Practice: The scale on a map shows one inch = 60 feet. Using the scale factor, find the distance 3¾ in. represents. x 3¾ 60 1 =

10. Practice: The scale on a map shows one inch = 60 feet
Practice: The scale on a map shows one inch = 60 feet. Using the scale factor, find the distance 5/8 in. represents. x
5/8 60 1 =

11. Practice: The scale on a map shows one inch = 60 feet
Practice: The scale on a map shows one inch = 60 feet. Using the scale factor, find the inches needed to represent 540 ft.
540 x 60 1 =

12. Practice: The scale on a map shows one inch = 60 feet
Practice: The scale on a map shows one inch = 60 feet. Using the scale factor, find the inches needed to represent 45 ft. 45 x 60 1 =

13. Practice: A triangular section of a city occupies 27 acres and is divided at even intervals by Pine St. and Maple St., which are parallel to Oak St. and perpendicular to Orange Ave. Find the area of each section A, B, and C.

14. P T S U V R Q
Oak St.
Maple St.
Orange St.
Pine St.

15. Homework pp

16. ►A. Exercises
The scale on a map shows 5 miles represented by 2 inches. Make a ratio as a scale factor and then answer the questions below.
1. What does one inch represent?

17. ►A. Exercises
The scale on a map shows 5 miles represented by 2 inches. Make a ratio as a scale factor and then answer the questions below.
3. What distance corresponds to seven inches on the map?

18. ►A. Exercises
The scale on a map shows 5 miles represented by 2 inches. Make a ratio as a scale factor and then answer the questions below.
5. How does the map represent three miles?

19. ►B. Exercises
7. Al is an archaeologist and is trying to find the height of a pyramid that he is studying. If he uses the mirror technique described in example 1, he must stand 8 feet from the mirror that is placed 640 feet from the center of the pyramid. Al’s eyes are approximately 6 feet from the ground. How high is the pyramid?

20. ►B. Exercises 7.

21. ►B. Exercises
9. Dan is standing at an observation deck on top of Pine Mountain, which is 5,872 feet high. From this viewpoint Dan can see a river on the far side of Buck Ridge (as shown). If Buck Ridge is 2,936 feet high and 4,875 feet from the river, how far from the river is Pine Mountain?

22. ■ Cumulative Review
Match the shape of each symbol (numeral or dash) to its classification.
21. 6
Simple Closed Curve
Simple Curve (not closed)
Closed Curve (not simple)
Curve (neither simple nor closed)
Not a curve

23. ■ Cumulative Review
Match the shape of each symbol (numeral or dash) to its classification.
22. –
Simple Closed Curve
Simple Curve (not closed)
Closed Curve (not simple)
Curve (neither simple nor closed)
Not a curve

24. ■ Cumulative Review
Match the shape of each symbol (numeral or dash) to its classification.
23. 0
Simple Closed Curve
Simple Curve (not closed)
Closed Curve (not simple)
Curve (neither simple nor closed)
Not a curve

25. ■ Cumulative Review
Match the shape of each symbol (numeral or dash) to its classification.
24. 30
Simple Closed Curve
Simple Curve (not closed)
Closed Curve (not simple)
Curve (neither simple nor closed)
Not a curve

26. ■ Cumulative Review
Match the shape of each symbol (numeral or dash) to its classification.
25. 8
Simple Closed Curve
Simple Curve (not closed)
Closed Curve (not simple)
Curve (neither simple nor closed)
Not a curve