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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. mKBL 5 ? 31. mDBK 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. mLBD 1 mDBK 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. 214 441198_C3_Ch7_WKbk_Ver-2.indd 214 b. mBFC 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 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 4 D 216 441198_C3_Ch7_WKbk_Ver-2.indd 216 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? © Pearson Education, Inc., publishing as Pearson Prentice Hall. 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 218 441198_C3_Ch7_WKbk_Ver-2.indd 218 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? 220 441198_C3_Ch7_WKbk_Ver-2.indd 220 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 mQ? 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 mPMQ. 222 441198_C3_Ch7_WKbk_Ver-2.indd 222 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. 224 441198_C3_Ch7_WKbk_Ver-2.indd 224 Course 3 Lesson 7-6 Guided Problem Solving 10/12/12 11:52 AM