Download 7-1 • Guided Problem Solving

Name
Class
Date
7-1 • Guided Problem Solving
GPS
Student Page 217, Exercises 28–31:
T
Use the diagram for Exercises 28–31.
L
28. LBD and TBL are ? angles.
140
64
D
R
B
K
29. RBT and  ? are vertical angles. 30. mKBL 5 ? 31. mDBK 5 ?
Understand
All rights reserved.
1. What are you asked to do?
2. What is true about the measures of two vertical angles?
3. What are adjacent angles?
Plan and Carry Out
4. Do angles LBD and TBL share a side? If so, what is it?
5. What type of angles are LBD and TBL? 6. What pairs of vertical angles are formed by the intersection of
* ) * )
TK and RL?
7. What is the measure of angle KBL?
8. mLBD 1 mDBK 5 10. Substitute what you know into the
equation in step 8 and solve.
9. Which angle is adjacent to LBD?
Check
11. Explain how to check your answer in Step 10.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
C
Solve Another Problem
12. Use the diagram at the right to solve.
a. CFA and DFE are ? angles.
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b. mBFC 5 ? °
D
85°
B 75° F
E
A
Course 3 Lesson 7-1
Guided Problem Solving
10/10/12 5:43 PM
Name
Class
Date
7-2 • Guided Problem Solving
GPS
Student Page 221, Exercise 31:
P
* )* )
a. In the diagram at the right, PQ || ST . Find the measure of each
numbered angle.
Q
80°
60°
b. What is the sum of the angle measures of the triangle?
Understand
1
2
3
S
T
All rights reserved.
1. What are alternate interior angles?
2. What are you asked to do?
Plan and Carry Out
3. Use angle 1 and angle 3 to name two pairs of alternate interior angles.
4. What is true of the measure of alternate interior angles?
5. What is the measure of angle 1?
6. What is the measure of angle 3?
7. What type of angle do angles 1, 2 and 3 form?
8. How many degrees are in a straight angle?
9. Use the information from Steps 5 and 6 to
help find the measure of angle 2.
10. What is the sum of the angle measures in
the triangle?
Check
11. Explain your answer from Step 10.
A
C
50°
3
Solve Another Problem
* )* )
12. In the diagram, AB || CD. Find the measure of each numbered angle.
2
B
110°
1
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4
D
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Course 3 Lesson 7-2
Guided Problem Solving
10/10/12 5:43 PM
Name
Class
Date
7-3 • Guided Problem Solving
Student Page 226, Exercises 24–27:
Maps Use the map at right for Exercises 24–27.
25. Copy the triangles. Mark
the sides and angles to
show congruent corresponding parts. 26. How far is Porter Square
from the intersection
of Lee Street and
Washington Road?
27. Find the distance along
the road from Porter
Square to Green Street.
0.18 km
Lee St.
24. Show that the triangles
in the map are
congruent.
Green St.
0.13 km
28
Porter Square
Su
mm
i
0.18 km t Av
e.
0.22 km
Washington Rd.
All rights reserved.
GPS
28
Understand
1. What methods can be used to show that two triangles are congruent?
Plan and Carry Out
2. How can you find the length of a missing
side?
4. Are the two triangles congruent? Why?
5. Sketch the two triangles. Mark their
corresponding parts.
6. How far is Porter Square from the intersection
of Lee Street and Washington Road?
8. Using your answer from Step 7, how can
you find the distance from Porter Square to
Green Street?
7. What is the total length of the street from
Washington to Green by the way of Porter
Square? Check
9. How could you show that these triangles are congruent by another method?
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3. What is the total length of the missing
hypotenuse?
Solve Another Problem
10. Explain why the pair of triangles shown are congruent.
Find the missing measures in the diagram.
A
6m
70°
43°
z
C
8m
8m
B D
y
8.2 m
E
70°
6m
x
F
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Course 3 Lesson 7-3
Guided Problem Solving
10/10/12 5:43 PM
Name
Class
Date
7-4 • Guided Problem Solving
GPS
Student Page 231, Exercise 15:
Clothing A T-shirt comes in different sizes.A large T-shirt is
21.5 in. wide and 26.5 in. long. If a small T-shirt is 15.5 in. wide, what is its length to the nearest inch?
Understand
1. What are you being asked to find? All rights reserved.
2. What type of relationship exists between the two shirts?
Plan and Carry Out
3. What are the dimensions of the large T-shirt?
4. What is the ratio of the width to the length of the large T-shirt?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. Set up a proportion for the situation. Let y equal the length of
the small T-shirt.
6. How will you solve for the variable y?
7. What is the value of y?
Check
8. Does your answer show that the two T-shirt sizes are
proportional?
Solve Another Problem
9. An artist wants to paint two proportional rectangular paintings
on canvas. One painting is larger than the other. The large painting is 20 in. wide and 8 in. long. The smaller painting is 16 in. wide and 6 in. long. Are the two paintings proportional in size?
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Course 3 Lesson 7-4
Guided Problem Solving
10/12/12 11:40 AM
Name
Class
Date
7-5 • Guided Problem Solving
GPS
Proving Triangles Similar
Student Page 235, Exercise 13:
City workers are laying out the paths in a new park, as shown in the diagram.
Do the workers have enough information to determine mQ?
If so, explain how to find its measure. If not, explain why not.
Understand
P
N
45°
60°
M
1. What are you being asked to find?
Q
All rights reserved.
2. What is the angle measure of a right angle?
3. How many pairs of corresponding angles must be congruent in
order for two triangles to be similar?
Plan and Carry Out
4. What angle measures does the diagram provide?
NMP 5
MPQ 5
NMQ 5
6. Now that you know the measure of two angles in
MQP, use angle sum of a triangle to find Q.
PMQ 5 NMQ 2 NMP 5
180° 2 (PMQ 1 MPQ) 5 Q 5
7. Is MQP  PNM? How do you know?
Check
8. Given the angle measure you found for Q, what is the angle sum
of MQP? Show each angle measure Solve Another Problem
9. For part of a theater set, students are supposed to build two similar
triangular wood frames. The first frame has the following side/angle/side
measure: 20 cm/80°/24 cm. The second frame has a different side-angle-side
measures: 15 cm/80°/18 cm. Are the frames similar triangles? Explain.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. Based on the angle measures shown in the diagram,
you can find mPMQ.
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Course 3 Lesson 7-5
Guided Problem Solving
10/12/12 11:52 AM
Name
Class
Date
7-6 • Guided Problem Solving
GPS
Student Page 243, Exercise 28:
The measures of six angles of a heptagon are 145°, 115°, 152°, 87°,
90°, and 150°. Find the measure of the seventh angle.
Understand
1. How many sides does a heptagon have? All rights reserved.
2. How many interior angles does a heptagon have?
3. What are you asked to find?
Plan and Carry Out
4. For a polygon with n sides, the sum of the measures of the
interior angles is (n 2 2)180°. Substitute what you know into the
formula to find the sum of the interior angles. Show your work.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. Find the total of the measures of the six interior angles given in
the problem.
6. Subtract the total you found in Step 5 from the total number of
degrees in a heptagon that you found in Step 4.
Check
7. Add all seven angles to verify that they total 900°.
Solve Another Problem
8. A decagon has interior angle measures of 156°, 178°, 124°, 132°,
138°, 142°, 116°, 178°, and 159°. Find the measure of the missing
angle.
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Course 3 Lesson 7-6
Guided Problem Solving
10/12/12 11:52 AM