Name
Class
Date
6-1 • Guided Problem Solving
GPS
Student Page 219, Exercise 17:
Writing in Math Can an angle ever have the same measure as its
complement? Explain.
Understand
1. What are you being asked to do?
All rights reserved.
2. What do you have to do to explain your answer?
Plan and Carry Out
3. What is the definition of complementary angles?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4. If an angle and its complement have the same measure, explain
the relationship between the angle and 90°.
5. Determine the measure of the angle.
6. Can an angle ever have
the same measure as its complement?
Check
7. Explain your answer.
Solve Another Problem
8. Can an angle ever have the same measure as its supplement?
Explain.
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Course 2 Lesson 6-1
Guided Problem Solving
10/10/12 2:21 PM
Name
Class
Date
6-2 • Guided Problem Solving
GPS
Student Page 226, Exercise 22:
Geography The shape of the state of Tennessee is similar to a
parallelogram. Estimate the area of Tennessee.
Understand
1. What are you being asked to do?
All rights reserved.
2. What shape is Tennessee similar to?
3. How do you find the area of a parallelogram?
Plan and Carry Out
4. What is the height of Tennessee? © Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. What is the length of the base of Tennessee? 6. Substitute the values into the formula A 5 bh. 7. What is the approximate area of Tennessee? Check
8. Is this estimate more or less than the actual area of Tennessee?
Explain.
Solve Another Problem
9. Tamika’s yard is similar to the shape of a parallelogram.
Estimate the area of Tamika’s yard.
175 ft
125 ft
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Course 2 Lesson 6-2
Guided Problem Solving
10/16/12 2:47 PM
Name
Class
Date
6-3 • Guided Problem Solving
GPS
Student Page 231, Exercise 22:
Two equilateral triangles with sides of length 6 inches are joined
together to form a rhombus. What is the perimeter of the rhombus?
Understand
1. What are you being asked to do? All rights reserved.
2. How do you measure the perimeter of a figure?
3. What is an equilateral triangle? Plan and Carry Out
4. In the space to the right, draw an equilateral triangle.
Label all of its sides as 6 in.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. Draw another equilateral triangle touching the first equilateral
triangle so that the two triangles form a rhombus.
6. Label the sides of the second triangle as 6 in.
7. Add the lengths of the sides of the rhombus to find the
perimeter. Check
8. Count the number of sides that the rhombus has. Multiply this
number by the length of the sides. Is this number the
same as your answer? Solve Another Problem
9. Two right isosceles triangles with legs of 5 in. length and a
hypotenuse of 7.1 in. are joined together to make a square.
What is the perimeter of the square?
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Course 2 Lesson 6-3
Guided Problem Solving
10/11/12 9:36 AM
Name
Class
Date
6-4 • Guided Problem Solving
GPS
Student Page 236, Exercise 17:
Music A hammer dulcimer is shaped like a trapezoid.The top edge
is 17 in. long, and the bottom edge is 39 in. long.The distance from the
top edge to the bottom edge is 16 in.What is the area of the
dulcimer?
Understand
All rights reserved.
1. Circle the information you will need to solve the problem.
2. What are you being asked to do?
3. How do you find the area of a trapezoid?
Plan and Carry Out
4. What is the height of the dulcimer? © Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. What are the bases of the dulcimer? 6. Substitute the values for the bases and
the height into the formula for area. 7. What is the area of the dulcimer? Check
8. Explain how you chose which measurements are the bases.
Solve Another Problem
9. Suppose the dulcimer had bases of 20 in. and 36 in. with the same
height. What would be the area of the dulcimer? How do the areas
compare? Explain.
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Course 2 Lesson 6-4
Guided Problem Solving
10/10/12 2:21 PM
Name
Class
Date
6-5 • Guided Problem Solving
GPS
Student Page 241, Exercise 29:
Bicycles The front wheel of a high-wheel bicycle from the late 1800s
was larger than the rear wheel to increase the bicycle’s overall
speed. The front wheel measured in height up to 60 in. Find the
circumference and area of the front wheel of a high-wheel bicycle.
Understand
All rights reserved.
1. Circle the information you will need to solve.
2. In the space to the right, draw a sketch of the bicycle that the
problem is discussing.
3. What are you being asked to do?
Plan and Carry Out
4. What is the diameter of the front wheel?
5. What is the radius of the front wheel?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
6. How do you find the circumference of a circle?
7. What is the circumference of the front wheel?
8. How do you find the area of a circle?
9. What is the area of the front wheel?
Check
10. How do you determine the radius if you know the area and
circumference of a circle?
Solve Another Problem
11. The diameter of a normal front wheel on a bicycle is 24 in.
Find the circumference and area of the front wheel.
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Course 2 Lesson 6-5
Guided Problem Solving
10/10/12 2:21 PM