Chapter 3 Parallel and Perpendicular Lines Key. c = \(\frac{9}{2}\) Justify your conjecture. The equation of the line along with y-intercept is: Hence, So, Answer: Hence, We can conclude that 8 right angles are formed by two perpendicular lines in spherical geometry. The given figure is: Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) The equation for another line is: We have to find the distance between X and Y i.e., XY A (x1, y1), and B (x2, y2) In Exercises 3-6, find m1 and m2. m is the slope So, So, Hence, from the above, Prove c||d Here 'a' represents the slope of the line. Hence, from the above, Answer: From the given figure, You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. Now, Step 4: y = \(\frac{1}{2}\)x + 6 So, Answer: We know that, AO = OB Now, d = \(\sqrt{(11) + (13)}\) 2x = 180 72 Name them. y = -3x + 150 + 500 P(0, 0), y = 9x 1 Now, -x + 4 = x 3 In Exercises 11-14, identify all pairs of angles of the given type. 2m2 = -1 Classify the pairs of lines as parallel, intersecting, coincident, or skew. From the above figure, Hence, from the above, c1 = 4 XY = 6.32 By using the parallel lines property, Question 25. Answer: Question 1. y = \(\frac{1}{3}\)x + c ERROR ANALYSIS 0 = \(\frac{1}{2}\) (4) + c So, Hence, Label the ends of the crease as A and B. P(- 7, 0), Q(1, 8) = \(\frac{45}{15}\) Each unit in the coordinate plane corresponds to 10 feet. The lines that have an angle of 90 with each other are called Perpendicular lines How are the slopes of perpendicular lines related? 1 = 180 140 2x = -6 Parallel lines are always equidistant from each other. c = -4 A(- \(\frac{1}{4}\), 5), x + 2y = 14 The slope of horizontal line (m) = 0 We can conclude that the perpendicular lines are: Perpendicular lines have slopes that are opposite reciprocals. The line l is also perpendicular to the line j Hence, from the above, Decide whether it is true or false. In the parallel lines, Explain our reasoning. Given 1 3 Substitute the given point in eq. We can conclude that Compare the given points with From the given figure, c = -3 The slopes are equal fot the parallel lines The equation for another line is: Explain. According to Corresponding Angles Theorem, \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) Now, Give four examples that would allow you to conclude that j || k using the theorems from this lesson. The coordinates of line b are: (3, -2), and (-3, 0) d = | x y + 4 | / \(\sqrt{2}\)} P = (22.4, 1.8) Which theorem is the student trying to use? We know that, The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. So, Hence, from the above, The equation of the parallel line that passes through (1, 5) is Hence, from the above, By comparing eq. Write the equation of the line that is perpendicular to the graph of 53x y = , and Parallel to \(6x\frac{3}{2}y=9\) and passing through \((\frac{1}{3}, \frac{2}{3})\). \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). We can conclude that 2 and 7 are the Vertical angles, Question 5. Vertical and horizontal lines are perpendicular. The given point is: A (3, -1) P || L1 The representation of the given point in the coordinate plane is: Question 56. The coordinates of line c are: (4, 2), and (3, -1) as shown. Explain your reasoning. Answer: In Exercises 17-22, determine which lines, if any, must be parallel. We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. So, d = 364.5 yards MATHEMATICAL CONNECTIONS Question 31. The Converse of the consecutive Interior angles Theorem states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. y= 2x 3 Answer: m1 m2 = \(\frac{1}{2}\) 2 Question 38. If the pairs of alternate exterior angles. y = mx + c The product of the slopes of perpendicular lines is equal to -1 The angles formed at all the intersection points are: 90 From the given figure, Substitute (1, -2) in the above equation The given point is: A (2, 0) VOCABULARY In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also Now, m = 3 d = \(\sqrt{(x2 x1) + (y2 y1)}\) By using the Perpendicular transversal theorem, Question 43. Answer: In Exercises 15 and 16, prove the theorem. Now, All its angles are right angles. So, We know that, We know that, The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar Simply click on the below available and learn the respective topics in no time. We can conclude that the line that is perpendicular to \(\overline{C D}\) is: \(\overline{A D}\) and \(\overline{C B}\), Question 6. To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles The coordinates of line 1 are: (10, 5), (-8, 9) It is given that m || n Now, The given point is: (4, -5) The point of intersection = (\(\frac{7}{2}\), \(\frac{1}{2}\)) y = \(\frac{1}{2}\)x 3 Your friend claims that lines m and n are parallel. We can observe that \(\overline{D H}\) and \(\overline{F G}\) 9 0 = b We know that, Label its intersection with \(\overline{A B}\) as O. Answer: Question 8. The product of the slopes of perpendicular lines is equal to -1 We can conclude that, Slope of AB = \(\frac{5}{8}\) Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. For a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1 In other words, if \(m=\frac{a}{b}\), then \(m_{}=\frac{b}{a}\). Imagine that the left side of each bar extends infinitely as a line. Answer: y = x 6 -(1) 2x = 7 Answer: Question 36. Find the slope \(m\) by solving for \(y\). The given figure is: Answer: Question 32. We can conclude that the midpoint of the line segment joining the two houses is: These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a parallel line passing through a given equation and point. X (-3, 3), Z (4, 4) line(s) perpendicular to m || n is true only when 147 and (x + 14) are the corresponding angles by using the Converse of the Alternate Exterior Angles Theorem 2x = 135 15 ATTENDING TO PRECISION y = \(\frac{1}{3}\)x \(\frac{8}{3}\). (y + 7) = (3y 17) \(\overline{C D}\) and \(\overline{A E}\) The standard linear equation is: When we compare the given equation with the obtained equation, Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting x = \(\frac{4}{5}\) We know that, = 180 76 Substitute (-1, -1) in the above equation These worksheets will produce 10 problems per page. A (x1, y1), and B (x2, y2) FCA and __________ are alternate exterior angles. = 4 Answer: Hence, from the above, From the given figure, The portion of the diagram that you used to answer Exercise 26 on page 130 is: Question 2. 3.12) y = mx + b c is the y-intercept Answer: MAKING AN ARGUMENT The slopes are equal fot the parallel lines EG = \(\sqrt{(5) + (5)}\) (11y + 19) and 96 are the corresponding angles What is m1? b. Explain your reasoning. We know that, You can refer to the answers below. y = 4x 7 m2 = -2 From the given figure, One answer is the line that is parallel to the reference line and passing through a given point. Hence, from the above, Algebra 1 worksheet 36 parallel and perpendicular lines answer key. m2 = \(\frac{1}{2}\) The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. Substitute (-1, -9) in the above equation = \(\sqrt{2500 + 62,500}\) The completed table of the nature of the given pair of lines is: Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal. Your friend claims the uneven parallel bars in gymnastics are not really Parallel. The flow proof for the Converse of Alternate exterior angles Theorem is: The symbol || is used to represent parallel lines. Question 11. The equation for another perpendicular line is: To find the value of c, y = \(\frac{1}{2}\)x 4, Question 22. The equation of the line along with y-intercept is: Prove 1, 2, 3, and 4 are right angles. The product of the slopes of the perpendicular lines is equal to -1 1 and 3 are the vertical angles Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent y = mx + c y = \(\frac{2}{3}\) So, We know that, If the slope of one is the negative reciprocal of the other, then they are perpendicular. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. (1) A(3, 4), y = x The equation that is perpendicular to the given line equation is: Name the line(s) through point F that appear skew to . Hence, from the above, According to the Perpendicular Transversal theorem, The slope of PQ = \(\frac{y2 y1}{x2 x1}\) We can observe that If two lines are horizontal, then they are parallel In Euclidean geometry, the two perpendicular lines form 4 right angles whereas, In spherical geometry, the two perpendicular lines form 8 right angles according to the Parallel lines Postulate in spherical geometry. Slope of ST = \(\frac{2}{-4}\) In Exploration 2. find more pairs of lines that are different from those given. y = -7x + c We can conclude that \(\frac{1}{3}\)x + 3x = -2 + 2 2x = 2y = 58 We can conclude that both converses are the same Hence, from the above, Perpendicular to \(x+7=0\) and passing through \((5, 10)\). Answer: So, We can observe that when r || s, So, Now, For a vertical line, 17x + 27 = 180 Write an equation of a line parallel to y = x + 3 through (5, 3) Q. The given table is: x = y =29 So, Substitute this slope and the given point into point-slope form. Explain your reasoning. We can conclude that the distance between the given 2 points is: 17.02, Question 44. So, Draw \(\overline{P Z}\), CONSTRUCTION Now, THINK AND DISCUSS 1. The representation of the parallel lines in the coordinate plane is: Question 16. The given figure is: For which of the theorems involving parallel lines and transversals is the converse true? 0 = 2 + c -2y = -24 Now, Explain. Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. We get, y = -2x + c Answer: b. Is b || a? Answer: We know that, A group of campers ties up their food between two parallel trees, as shown. Now, Question 25. The coordinates of line d are: (0, 6), and (-2, 0) y = \(\frac{1}{2}\)x + c From the given figure, So, c = 5 7 In Exploration 2. m1 = 80. Hence, 8 = \(\frac{1}{5}\) (3) + c Answer: By using the vertical Angles Theorem, Now, The slope that is perpendicular to the given line is: m2 = \(\frac{1}{2}\), b2 = 1 Explain. y = \(\frac{2}{3}\) Answer: Question 14. The diagram that represents the figure that it can be proven that the lines are parallel is: Question 33. The intersection of the line is the y-intercept c = 5 y = 3x 6, Question 11. We know that, Answer: Explain your reasoning. So, We know that, x = \(\frac{69}{3}\) We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{1}{m_{2}}\). The given figure is: So, We know that, Does either argument use correct reasoning? Solution: Using the properties of parallel and perpendicular lines, we can answer the given . Identify all pairs of angles of the given type. So, Answer: Q1: Find the slope of the line passing through the pairs of points and describe the line as rising 745 Math Consultants 8 Years on market 51631+ Customers Get Homework Help The product of the slopes of the perpendicular lines is equal to -1 (B) Alternate Interior Angles Converse (Thm 3.6) Identifying Parallel, Perpendicular, and Intersecting Lines from a Graph Explain your reasoning. Find equations of parallel and perpendicular lines. These worksheets will produce 6 problems per page. y = 4x + b (1) The perimeter of the field = 2 ( Length + Width) We can say that any parallel line do not intersect at any point So, Now, Answer: Explain your reasoning. So, So, Hence, from the above, Question 3. From the above figure, Question 13. By using the Alternate Exterior Angles Theorem, Answer: Now, m1 m2 = -1 c. m5=m1 // (1), (2), transitive property of equality So, We know that, What is the distance between the lines y = 2x and y = 2x + 5? We know that, The lines perpendicular to \(\overline{E F}\) are: \(\overline{F B}\) and \(\overline{F G}\), Question 3. 68 + (2x + 4) = 180 The parallel line equation that is parallel to the given equation is: -2 \(\frac{2}{3}\) = c Hence, from the above, Parallel and perpendicular lines have one common characteristic between them. Answer: By comparing the slopes, c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. y = -2x + c Your school lies directly between your house and the movie theater. \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines Question 4. From the above figure, The equation of a line is: We can conclude that the distance from point A to the given line is: 2.12, Question 26. Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 c = 3 This can be proven by following the below steps: From the given figure, From the above diagram, -4 = \(\frac{1}{2}\) (2) + b We can observe that List all possible correct answers. Answer: Question 12. The equation of line p is: We know that, The given figure is: Is your friend correct? The given point is: A (-3, 7) Hence, from the above, The given lines are: Explain your reasoning. Which pair of angle measures does not belong with the other three? The distance between the given 2 parallel lines = | c1 c2 | The given equation is: Substitute A (-2, 3) in the above equation to find the value of c So, The slope of the horizontal line (m) = \(\frac{y2 y2}{x2 x1}\) 8x = 112 The distance from point C to AB is the distance between point C and A i.e., AC Justify your answer for cacti angle measure. Negative reciprocal means, if m1 and m2 are negative reciprocals of each other, their product will be -1. m = \(\frac{5}{3}\) The Coincident lines may be intersecting or parallel The diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal We have seen that the graph of a line is completely determined by two points or one point and its slope. k = -2 + 7 4 and 5 b.) We have to find the point of intersection When we compare the given equation with the obtained equation, m1 m2 = -1 Answer: Question 32. Parallel to \(2x3y=6\) and passing through \((6, 2)\). 10. Prove the statement: If two lines are vertical. Question 5. From the given figure, m2 = -2 The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. Which rays are parallel? Slope of QR = \(\frac{1}{2}\), Slope of RS = \(\frac{1 4}{5 6}\) The slopes are the same but the y-intercepts are different Answer: The perpendicular lines have the product of slopes equal to -1 c = -2 b is the y-intercept c = 2 The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) c = -2 Perpendicular lines are those lines that always intersect each other at right angles. y = 2x The given figure is: The lines that do not have any intersection points are called Parallel lines The given point is: (1, -2) Hence, from the above, In Exercises 15 and 16, use the diagram to write a proof of the statement. For parallel lines, Substitute A (6, -1) in the above equation If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. m = \(\frac{3 0}{0 + 1.5}\) and N(4, 1), Is the triangle a right triangle? From the given figure, x and 97 are the corresponding angles Use these steps to prove the Transitive Property of Parallel Lines Theorem Now, Answer: So, CRITICAL THINKING a = 2, and b = 1 The slope of first line (m1) = \(\frac{1}{2}\) These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel lines from pictures. x = 40 11 and 13 Question 18. a. So, Substitute A (3, -4) in the above equation to find the value of c (D) Question 1. A(1, 3), B(8, 4); 4 to 1 y = -2x + c We can conclude that the value of x is: 54, Question 3. From the given graph, We can say that w and x are parallel lines by Perpendicular Transversal theorem. Explain why the tallest bar is parallel to the shortest bar. b. m1 + m4 = 180 // Linear pair of angles are supplementary It is given that m || n 2x x = 56 2 A (x1, y1), B (x2, y2) a.) If you need more of a review on how to use this form, feel free to go to Tutorial 26: Equations of Lines 1. We can conclude that We know that, (a) parallel to the line y = 3x 5 and To be proficient in math, you need to communicate precisely with others. From the given figure, The given equations are: Determine whether the converse is true. Question 3. For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. Answer: Identify the slope and the y-intercept of the line. We know that, Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. We get To find the value of c, The given figure is: x = \(\frac{87}{6}\) In Exercises 9 and 10, trace \(\overline{A B}\). c = 6 0 So, The equation that is perpendicular to the given line equation is: ERROR ANALYSIS We know that, CONSTRUCTING VIABLE ARGUMENTS y = -2x + 2, Question 6. We know that, The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) The given points are: Now, Compare the given points with (x1, y1), (x2, y2) We can conclude that the linear pair of angles is: Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. = \(\sqrt{(9 3) + (9 3)}\) The postulates and theorems in this book represent Euclidean geometry. We know that, 1 = 2 Answer: The given pair of lines are: Now, y = -2x + c Given m1 = 105, find m4, m5, and m8. Answer: Question 2. It is given that in spherical geometry, all points are points on the surface of a sphere. We can conclude that A(0, 3), y = \(\frac{1}{2}\)x 6 4. Perpendicular to \(y=2x+9\) and passing through \((3, 1)\). Unit 3 (Parallel & Perpendicular Lines) In this unit, you will: Identify parallel and perpendicular lines Identify angle relationships formed by a transversal Solve for missing angles using angle relationships Prove lines are parallel using converse postulate and theorems Determine the slope of parallel and perpendicular lines Write and graph Substitute A (0, 3) in the above equation 5 = 4 (-1) + b From the given figure, y = mx + b d = | 6 4 + 4 |/ \(\sqrt{2}\)} We know that, So, A(- 3, 7), y = \(\frac{1}{3}\)x 2 x = \(\frac{18}{2}\) Now, Which lines(s) or plane(s) contain point G and appear to fit the description? Answer: 3y + 4x = 16 We can conclude that there are not any parallel lines in the given figure. The perpendicular lines have the product of slopes equal to -1 Explain. ABSTRACT REASONING Line 2: (7, 0), (3, 6) So, \(\frac{1}{2}\) . So, These worksheets will produce 6 problems per page. Answer: So, Given m1 = 115, m2 = 65 x + 2y = 2 Now, Possible answer: plane FJH plane BCD 2a. The equation that is perpendicular to the given line equation is: What are Parallel and Perpendicular Lines? The slopes of the parallel lines are the same Answer: So, y = 3x + c Each unit in the coordinate plane corresponds to 10 feet We can conclude that quadrilateral JKLM is a square. CONSTRUCTING VIABLE ARGUMENTS x = 35 Answer: Answer: Hence, from the above, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) Use the Distance Formula to find the distance between the two points. So, We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. Hence, from the above, The equation that is perpendicular to the given line equation is: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. Explain why or why not. c = 7 From the given coordinate plane, We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles So, -1 = 2 + c 2x = 108 So, Then by the Transitive Property of Congruence (Theorem 2.2), 1 5. Question 35. 3: write the equation of a line through a given coordinate point . Draw the portion of the diagram that you used to answer Exercise 26 on page 130. We know that, a. y = \(\frac{1}{3}\)x + c 2x + y + 18 = 180 AB = AO + OB x = 0 The converse of the given statement is: The product of the slopes is -1 and the y-intercepts are different 3.3). Question 25. 1 4. Answer: The given point is: (6, 1) Answer: Question 2. 11y = 96 19 (13, 1), and (9, -4) 4x + 2y = 180(2) The given lines are: We can observe that a is perpendicular to both the lines b and c Identify two pairs of perpendicular lines. \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) y = 144 ANALYZING RELATIONSHIPS m is the slope = \(\sqrt{(3 / 2) + (3 / 2)}\) So, Explain your reasoning. Explain your reasoning. So, PROVING A THEOREM Click here for More Geometry Worksheets So, Substitute (4, -5) in the above equation = \(\frac{0 + 2}{-3 3}\) If two lines are parallel to the same line, then they are parallel to each other Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. Given: 1 and 3 are supplementary The parallel line equation that is parallel to the given equation is: 2x = \(\frac{1}{2}\)x + 5 So, We can conclude that the value of x is: 107, Question 10. We can observe that the length of all the line segments are equal Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(1: m1m2=1\). b. m1 + m4 = 180 // Linear pair of angles are supplementary 9 = \(\frac{2}{3}\) (0) + b 8 = 105, Question 2. The product of the slopes of the perpendicular lines is equal to -1 x = 3 (2) plane(s) parallel to plane ADE y = \(\frac{1}{3}\)x 2. y= \(\frac{1}{3}\)x + 4 Answer: In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning. 1 = 4 Explain why the top step is parallel t0 the ground. (- 1, 5); m = 4 Converse: m = 2 The letter A has a set of perpendicular lines. y = 4 x + 2 2. y = 5 - 2x 3. (D) Consecutive Interior Angles Converse (Thm 3.8) x = 12 and y = 7, Question 3. XY = \(\sqrt{(6) + (2)}\) y = \(\frac{1}{2}\)x + c Hence, from the above, We can say that they are also parallel Proof of Converse of Corresponding Angles Theorem: x = 60 Hence, from the above, The product of the slopes is -1 Hence, from the above, Answer: Hence, Each unit in the coordinate plane corresponds to 50 yards. x + 2y = 2 Slope of AB = \(\frac{4}{6}\) What does it mean when two lines are parallel, intersecting, coincident, or skew? We know that, y = -x + c In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Hence, from the above, Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line We have to divide AB into 10 parts So, Answer: The given figure is: So, We know that, We can observe that when p || q, We can conclude that the value of x is: 133, Question 11. x = 14 The sides of the angled support are parallel. So, m = \(\frac{0 2}{7 k}\) = \(\frac{4}{-18}\) 5y = 3x 6 We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. We know that, Substitute A (-3, 7) in the above equation to find the value of c From the given figure, We know that, If we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0 The slope of the line that is aprallle to the given line equation is: We know that, So, (2x + 20)= 3x The lines that do not intersect or not parallel and non-coplanar are called Skew lines Hence, In this case, the negative reciprocal of 1/5 is -5. m = 2 1 = 32 Substitute P (3, 8) in the above equation to find the value of c 2x y = 18 The given equation in the slope-intercept form is: The given equation is: So, Answer: Connect the points of intersection of the arcs with a straight line. In Exercises 7-10. find the value of x. Name a pair of parallel lines. So, The angles that have the opposite corners are called Vertical angles If the support makes a 32 angle with the floor, what must m1 so the top of the step will be parallel to the floor?
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parallel and perpendicular lines answer key