Classwork Problems and Homework Packet - Unit 1

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1 Multi-Step Equations DIRECTIONS: Solve each equation. Name NOTE: All answers hav been provided. You are responsible for showing all the work to arrive at the correct answer listed. Date Period 1) 20 = 4x 6x {2} 2) 6 = 1 2n + 5 {0} 3) 8x 2 = 9 + 7x { 7} 4) a + 5 = 5a + 5 {0} 5) 4m 4 = 4m No solution. 6) p 1 = 5 p + 3p 8 {1} 7) 5p 14 = 8 p + 4 { 6} 8) p 4 = 9 + p No solution. 9) 8 = (x + 4) {4} 10) 12 = 4( 6x 3) {0} 11) 14 = (p 8) { 6} 12) (7 4x) = 9 {4} 13) 18 6k = 6(1 + 3k) { 1} 14) 5n + 34 = 2(1 7n) {4} 15) 2(4x 3) 8 = 4 + 2x {3} 16) 3n 5 = 8(6 + 5n) { 1} 17) (1 + 7x) 6( 7 x) = 36 {5} 18) 3(4x + 3) + 4(6x + 1) = 43 {4} 19) 24a 22 = 4(1 6a) 20) 5(1 5x) + 5( 8x 2) = 4x 8x No solution. { 5} Classwork Problems and Homework Packet - Unit 1 pg. 1 k l2t011k2u KKIuutua7 qs7ocfotbwmadrlel ulxl5c8.h 4 2Aaldl0 srsibgohct7su QrieXsZe6rzvPeBdB.V c HM9aJdIef Qwzihtdhb xinnnfaivnbi3tseg zaal3gdevbxr3ad w1r.o Worksheet by Kuta Software LLC

diagram 2. Name four points 3. Name two lines 4.

2 Unit 1 Homework - Topic 1 & 2 Points, Lines & Planes Name Period 1. Explain the difference between COLLINEAR and COPLANAR: Collinear: Coplanar: For #2 5, use the diagram 2. Name four points 3. Name two lines 4. Name the plane that contains points A, B, and C 5. Name the plane that contains points A, D, and E 6. Describe and correct the error in naming opposite rays in the diagram. pg. 2

Name a point that is not coplanar with R, S, and T For #11 14, use the diagram that shows a molecule of Phosphorus

3 For #7 10, use the diagram below 7. Give two other names for WQ 8. Give another name for plane V 9. Name three points that are collinear. Then name a fourth point that is not collinear with these three points 10. Name a point that is not coplanar with R, S, and T For #11 14, use the diagram that shows a molecule of Phosphorus Pentachloride 11. Name three points that are not collinear 12. Name two opposite rays 13. Give another name for JH 14. Name two different planes that contain HL pg. 3

4 For #15 20, use the diagram 15. What is another name for BD? 16. What is another name for AC? 17. What is another name for ray AE? 18. Name all rays with endpoint E 19. Name two pairs of opposite rays 20. Name one pair of rays that are not opposite rays For #21 28, sketch the figure described 21. Plane P and line l intersecting at one point 22. Plane K and line m intersecting at all points on line m pg. 4

5 23. AB and AC 24. MN and NX 25. Plane M and NB intersecting at B 26. Plane M and NB intersecting at A 27. Plane A and plane B not intersecting 28. Plane C and plane D intersecting at XY For #29 30, use the diagram. 29. Name the intersection of plane AEH and plane FBE 30. Name the intersection of plane BGF and plane HDG pg. 5

6 For #31 36, use the diagram. Name a point that is 31. Collinear with points E and H 32. Collinear with points B and I 33. Not collinear with points E and H 34. Not collinear with points B and I 35. Coplanar with points D, A, and B 36. Coplanar with points C, G, and F 37. Given two points on a line and a third point not on the line, is it possible to draw a plane that includes the line and the third point? Draw a picture to explain your reasoning. 38. Is it possible for one point to be in two different planes? Draw a picture to explain your reasoning. 39. Explain why a four-legged chair may rock from side to side even if the floor is level. Would a three-legged chair on the same level floor rock from side to side? Why or why not? pg. 6

7 40. Name two points that are collinear with P 41. Name two planes that contain J 42. Name all the points that are in more than one plane For #43 46, name the geometric term modeled by the object pg. 7

8 Unit 1 Practice - Topic 1 & 2 - Segment Addition Postulate Lesson 1.2 Practice B For use with the lesson Use Segments and Congruence Measure the length of the segment to the nearest tenth of a centimeter. 1. A B 2. M N 3. E F Use the Segment Addition Postulate to find the indicated length. 4. Find RT. 5. Find BC. 6. Find MN R 17 S 8.5 T A 25 B C M N 26 P Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent. 7. A(2, 2), B(4, 2), C(21, 21), D(21, 1); 8. M(1, 23), N(4, 23), O(3, 4), P(4, 4); } AB and } CD MN } and } OP y y x 2 x Lesson E(23, 4), F(21, 4), G(2, 4), H(21, 1); 10. R(3, 5), S(10, 5), T(24, 23), U(211, 23); } EG and } FH } RS and } TU 1 y 1 x Use the number line to find the indicated distance. A B C D E AB 12. AD 13. CD 14. BD 15. CE 16. AE 17. BE 18. DE 3 y 3 x Copyright Houghton Mifflin Harcourt Publishing Company. All rights reserved. pg. 8

9 Lesson 1.2 Practice B continued For use with the lesson Use Segments and Congruence In the diagram, points A, B, C, and D are collinear, points C, X, Y, and Z are collinear, AB 5 BC 5 CX 5 YZ, AD 5 54, XY 5 22, and XZ Find the indicated length. 19. AB D 20. BD 21. CY 22. CD A B C X 23. XC 24. CZ Y Find the indicated length. 25. Find ST. 26. Find AC. 27. Find NP. Z 32 4x 1 4 6x 2 23 R 4x S 12x T A 14 B 3x 2 4 C M N 3x 1 2 P x 2 5 Copyright Houghton Mifflin Harcourt Publishing Company. All rights reserved. Point J is between H and K on } HK. Use the given information to write an equation in terms of x. Solve the equation. Then find HJ and JK. 28. HJ 5 2x 29. HJ 5 x } 4 JK 5 3x JK 5 3x 2 4 KH 5 25 KH HJ 5 5x HJ 5 5x 2 3 JK 5 8x 2 10 JK 5 x 2 9 KH 5 38 KH 5 5x 32. Hiking On the map, } AB represents a trail that you are hiking. You start from the beginning of the trail and hike for 90 minutes at a rate of 1.4 miles per hour. How much farther do you need to hike to reach the end of the trail? 1 Distance (mi) Rest Area A(3, 2) B(8.2, 2) Ranger Station 1 Distance (mi) Lesson 1.2 pg. 9

10 Unit 1 Homework - Topic 3 Using Midpoint Formulas Name Period For #1 2, find RS 1. RS = 2. RS = For #3 4, find x and JK 3. x = JK = 4. x = JK = For #5 6, find x and XY 5. x = XY = 6. x = XY = pg. 10

11 For #7 8, the endpoints of CD are given. Find the coordinates of the midpoint M. Draw and label the diagram, show all work. 7. C(3, 5) and D(7, 9) M = 8. C( 8, 6) and D( 4, 10) M = For #9 11, the midpoint M and one endpoint of GH are given. Find the coordinates of the other endpoint. Draw and label the diagram, show all work. *use either method* 9. G(5, 6) and M(4, 3) H = 10. H( 3, 7) and M( 2, 5) G = 11. H( 2, 9) and M(8, 0) G = pg. 11

12 12. In baseball, the strike zone is the region a baseball needs to pass through for the umpire to declare it a strike when the batter does not swing. The top of the strike zone is a horizontal plane passing through the midpoint of the top of the batter s shoulders and the top of the uniform pants when the player is in a batting stance. Find the height of T. All heights are in inches. T = 13. A house and a school are 5.7 kilometers apart on the same straight road. The library is on the same road, halfway between the house and the school. Draw and label the diagram. How far is the library from the house? Distance = 14. On a straight stretch of highway, a food exit is one fifth of the way between Exit 158 and Exit 178, where the exit numbers correspond to the location in miles along the highway. What is the exit number for the food exit? Exit Number = 15. The length of XY is 24 centimeters. The midpoint of XY is M, and C is on XM so that XC is 2/3 of XM. Point D is on MY so that MD is 3/4 of MY. What is the length of CD? Draw and label the diagram. Show all work. CD = pg. 12

13 Unit 1 Homework - Topic 4 Measuring & Constructing Segments (pt. 1) Name Period For #1 3, find the length of the segment 1. BD 2. AC 3. ED For #4 9, find the length FH 4. FH = 5. FH = 6. FH = 7. FH = 8. FH = 9. FH = pg. 13

14 10. What formula can be used to find the distance between the two points, or the length of a segment if you are given the coordinates of the endpoints? For #11 15, find the distance between the two points. Show all work, including the formula. Round to the nearest tenth if necessary. 11. A(13, 2) and B(7, 10) Distance = 12. C( 6, 5) and D( 3, 1) Distance = pg. 14

15 13. G( 5, 4) and H(2, 6) Distance = 14. R(0, 1) and S(6, 3.5) Distance = 15. J( 8, 0) and K(1, 4) Distance = pg. 15

A(0, 2) B( 3, 8) C( 2, 2) D(0, 4) Length AB = Length CD = 17.

16 For #16 17, plot the points in a coordinate plane then determine whether AB and CD are congruent. Show all work. 16. A(0, 2) B( 3, 8) C( 2, 2) D(0, 4) Length AB = Length CD = 17. A(1, 4) B(5, -1) C( 3, 1) D(1, 6) Length AB = Length CD = pg. 16

Unit 1 Homework - Topic 5 Supplement The Pythagorean Theorem Name Period 1. What is a Pythagorean Triple? For #2 5, find the value of x. Then decide whether the side lengths form a Pythagorean triple.

17 Unit 1 Homework - Topic 5 Supplement The Pythagorean Theorem Name Period 1. What is a Pythagorean Triple? For #2 5, find the value of x. Then decide whether the side lengths form a Pythagorean triple. 2. x = 3. x = Pythagorean Triple? Yes/No Pythagorean Triple? Yes/No 4. x = 5. x = Pythagorean Triple? Yes/No Pythagorean Triple? Yes/No 6. Describe and correct the error in using the Pythagorean Theorem pg. 17

7. The fire escape forms a right triangle, as shown.

The backboard of the basketball hoop forms a right triangle with the supporting rods, as

Use the Pythagorean Theorem to approximate the distance between the rods where they meet the

18 7. The fire escape forms a right triangle, as shown. Use the Pythagorean Theorem to approximate the distance between the two platforms. x = 8. The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate the distance between the rods where they meet the backboard. x = 9. You are making a kite and need to figure out how much binding to buy. You need the binding for the perimeter of the kite. The binding comes in packages of two yards. How many packages should you buy? pg. 18

19 For #10 13, decide whether the triangle is a right triangle. Show all work. 10. Right Triangle? Yes/No 11. Right Triangle? Yes/No 12. Right Triangle? Yes/No 13. Right Triangle? Yes/No For #14 17, verify that the segment lengths form a triangle. Then decide whether the triangle is acute, right, or obtuse. Show all work , 11, and , 20, and 36 Triangle? Yes/No Acute/Right/Obtuse Triangle? Yes/No Acute/Right/Obtuse , 30, and , 15, and 5 13 Triangle? Yes/No Acute/Right/Obtuse Triangle? Yes/No Acute/Right/Obtuse pg. 19

18. In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base.

Distance = For #19 20, find the area of the isosceles triangle. Show all work, including formulas. **A = 1/2 b h 19. Area = 20. Area = 21.

20 18. In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out? Draw and label the picture. Distance = For #19 20, find the area of the isosceles triangle. Show all work, including formulas. **A = 1/2 b h 19. Area = 20. Area = 21. How do you know C is a right angle without using the Pythagorean Theorem? 22. Your friend claims 72 and 75 cannot be part of a Pythagorean triple because does not equal a positive integer squared. Is your friend correct? Explain your reasoning pg. 20

21 Unit 1 Homework - Topic 4 Additional Practice Measuring & Constructing Segments (pt. 2) Name Period For #1 3, find the length of the segment 1. In 2003, a remote controlled model airplane became the first ever to fly nonstop across the Atlantic Ocean. The map shows the airplane s position at three different points during its flight. Point A represents Cape Spear, Newfoundland, point B represents the approximate position after 1 day, and point C represents Mannin Bay, Ireland. The airplane left from Cape Spear and landed in Mannin Bay. Show all work. a. Find the total distance the model airplane flew. Distance = b. The model airplane s flight lasted nearly 38 hours. Estimate the airplane s average speed in miles per hour. Average Speed = 2. You travel from City A to City B. You know that the round trip distance is 647 miles. City C, a city you pass on the way, is 27 miles from City A. Find the distance from City C to City B. Draw and label the picture. Distance = pg. 21

22 3. Your school is 20 blocks east and 12 blocks south of your house. The mall is 10 blocks north and 7 blocks west of your house. You plan on going to the mall right after school. Find the distance between your school and the mall assuming there is a road directly connecting the school and the mall. One block is 0.1 mile. Draw and label the diagram. Show all work. Distance = For #4 7, point S is between points R and T on RT. Use the given information to find the value of x, RS, ST, and RT. Draw and label the diagram. Show all work. 4. RS = 2x + 10 ST = x 4 RT = 21 x = RS = ST = RT = 5. RS = 3x 16 ST = 4x 8 RT = 60 x = RS = ST = RT = pg. 22

23 6. RS = 2x 8 ST = 11 RT = x + 10 x = RS = ST = RT = 7. RS = 4x 9 ST = 19 RT = 8x 14 x = RS = ST = RT = 8. In the diagram, AB = 1/2CD, CD = 2BC, and AD = 20 in. Find the lengths of all segments in the diagram. Suppose you choose one of the segments at random. What is the probability that the measure of the segment is less than 10? Show your work. AB = BC = AC = BD = CD = Probability = 9. Your friend claims there is an easier way to find the length of a segment than the Distance Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is subtract the y-coordinates. Do you agree with his statement? Explain your reasoning. Include an example. pg. 23

10. The figure shows the position of three players during part of a water polo match. Player A throws the ball to Player B, who then throws the ball to Player C. Show all work. a. How far did Player A throw the ball?

24 10. The figure shows the position of three players during part of a water polo match. Player A throws the ball to Player B, who then throws the ball to Player C. Show all work. a. How far did Player A throw the ball? Distance = b. How far did Player B throw the ball? Distance = c. How far would Player A have to throw the ball to throw it directly to Player C? Distance = pg. 24

25 11. A path goes around a triangular park, as shown. a. Find the distance around the entire park to the nearest yard. Distance = b. A new path and a bridge are constructed from point Q to the midpoint M of PR. Find the coordinates of M and QM. Round to the nearest yard. M = QM = c. A man jogs from P to Q to M to R to Q and back to P at an average speed of 150 yards per minute. About how many minutes will it take him? # of minutes = pg. 25

26 Unit 1 Homework - Topic 5 & 6 pg. 26

27 pg. 27

How are the slopes of perpendicular lines related? Include an example in your explanation.

28 Unit 1 Homework - Topic 7 Date Due Name Period Slopes of Lines 1. How are the slopes of parallel lines related? Include an example in your explanation. 2. How are the slopes of perpendicular lines related? Include an example in your explanation. For #3 8, find the slope of the line that passes through the given points. 3. Slope = 4. Slope = 5. Slope = 6. Slope = ( 5, 1), (3, 1) (2, 1), (0, 6) pg. 28

29 7. Slope = 8. Slope = ( 1, 4), (1, 2) ( 7, 0), ( 7, 6) For #9 12, using a ruler, graph the line through the given point with the given slope. 9. P(3, 2) m = 1/6 10. P( 4, 0) m = 5/2 11. P(0, 5) m = 2/3 12. P(2, 6) m = 7/4 pg. 29

Parallel Lines: Perpendicular Lines: 15.

30 For #13 14, determine which of the lines are parallel and which of the lines are perpendicular. 13. Parallel Lines: Perpendicular Lines: 14. Parallel Lines: Perpendicular Lines: 15. Carpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof. Slope = pg. 30

31 16. Describe and correct the error in determining whether the lines are parallel, perpendicular, or neither. For #17 20, determine whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. 17. Line 1: (1, 0), (7, 4) parallel/perpendicular/neither Line 2: (7, 0), (3, 6) 18. Line 1: ( 3, 1), ( 7, 2) parallel/perpendicular/neither Line 2: (2, 1), (8, 4) 19. Line 1: ( 9, 3), ( 5, 7) parallel/perpendicular/neither Line 2: ( 11, 6), ( 7, 2) 20. Line 1: (10, 5), ( 8, 9) parallel/perpendicular/neither Line 2: (2, 4), (11, 6) pg. 31

32 21. Determine whether quadrilateral JKLM is a square. Explain your reasoning. Slope KL = Slope LM = Slope MJ = Slope JK = Square? Yes/No Reasoning: 22. Given any 2 lines, how would you determine which line is steeper without graphing them? Include an example in your explanation. 23. Triangle LMN has vertices L(0, 6), M(5, 8), and N(4, 1). Is the triangle a right triangle? Explain your reasoning. Slope LM = Slope MN = Slope LN = Right Triangle? Yes/No Reasoning: pg. 32

33 For #24 29, identify the slope and y-intercept of the line Remember: put all equations into y = form first, in other words, solve for y. 24. y = 3x + 9 Slope = y-intercept = 25. y = x - 7 Slope = y-intercept = 26. 3x + 6y = 12 Slope = y-intercept = 27. y = -x Slope = y-intercept = 28. 2y = x + 8 Slope = y-intercept = 29. 2x + 3y = 5 Slope = y-intercept = pg. 33

34 Unit 1 Homework - Topic 8 Date Due Name Period Equations of Parallel and Perpendicular Lines For #1 4, write an equation of the line passing through point P that is parallel to the given line. Graph the equations of the lines to check that they are parallel. 1. P(0, 1) y = 2x + 3 Equation of the Line: 2. P(3, 4) y = 1/5(x + 4) Equation of the Line: 3. P( 2, 3) x = 5 Equation of the Line: pg. 34

35 4. P(4, 0) x + 2y = 12 Equation of the Line: For #5 8, write an equation of the line passing through point P that is perpendicular to the given line. Graph the equations of the lines to check that they are perpendicular. 5. P(0, 0) y = 3x 1 Equation of the Line: 6. P(4, 5) y = 3 Equation of the Line: pg. 35

36 7. P(2, 3) y 4 = 2(x + 3) Equation of the Line: 8. P( 4, 0) 3x 5y = 6 Equation of the Line: 9. Describe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1. pg. 36

37 10. A new road is being constructed parallel to train tracks through point S(3, 2). The equation of the line representing the train tracks is y = 2x. Find the equation of the line representing the new road. Equation of the Line: 11. A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). The equation of the line representing Washington Boulevard is y = 2/3x. Find the equation of the line representing the bike path. Equation of the Line: pg. 37

38 For #12 15, find the midpoint of PQ. Then write the equation of the line that passes through the midpoint and is perpendicular to PQ. 12. P( 4, 3) Q(4, 1) Equation of the Line: 13. P( 5, 5) Q(3, 3) Equation of the Line: pg. 38

39 14. P(0, 2) Q(6, 2) Equation of the Line: 15. P( 7, 0) Q(1, 8) Equation of the Line: pg. 39

40 16. Write an equation of the line passing through the point ( 8, 6) that is parallel to the line y = 4x 1 Equation of the Line: 17. Write an equation of the line passing through the point ( 20, 4) that is perpendicular to the line 2x + 5y = 10 Equation of the Line: pg. 40

41 18. Write an equation of the line passing through the point ( 8, 6) that is parallel to the line y = 4x 1 Equation of the Line: 19. Write an equation of the line passing through the point ( 20, 4) that is perpendicular to the line 2x + 5y = 10 Equation of the Line: pg. 41

Therefore, x is 3. BC = 2x = 2(3) = Line Segments and Distance. Find each measure. Assume that each figure is not drawn to scale. 1.

Therefore, x is 3. BC = 2x = 2(3) = 6. 1-2 Line Segments and Distance Find each measure. Assume that each figure is not drawn to scale. 1. CD Thus, BC is 6. 4. CB = 4x 9, BD = 3x + 5, and CD = 17 Here