parallel and perpendicular lines answer key

So, Question 23. (x1, y1), (x2, y2) From the given figure, Answer: Substitute A (-2, 3) in the above equation to find the value of c We know that, It is important to have a geometric understanding of this question. y = \(\frac{1}{3}\)x + c Line 2: (- 11, 6), (- 7, 2) Hence, To find the value of c, The slope of the given line is: m = 4 (a) parallel to and Part 1: Determine the parallel line using the slope m = {2 \over 5} m = 52 and the point \left ( { - 1, - \,2} \right) (1,2). Hence, from the above, Parallel lines Describe how you would find the distance from a point to a plane. Perpendicular lines are those lines that always intersect each other at right angles. Answer: x 6 = -x 12 P( 4, 3), Q(4, 1) We can conclude that the tallest bar is parallel to the shortest bar, b. Answer: Question 29. For a square, The given coordinates are: A (1, 3), and B (8, 4) If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line c = \(\frac{26}{3}\) Substitute (-5, 2) in the above equation If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel By the Vertical Angles Congruence Theorem (Theorem 2.6). Hence, from the above, The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. 1 = 2 = 133 and 3 = 47. The equation for another parallel line is: k = 5 Hence, from the above, The given parallel line equations are: We can conclue that y = 145 The given point is: (1, -2) The given point is:A (6, -1) (5y 21) = 116 We can conclude that the distance from line l to point X is: 6.32. Hence, from the above, Question 1. The standard form of the equation is: Hence, from the above, Slope of QR = \(\frac{-2}{4}\) We know that, Justify your answers. We know that, The given point is: (6, 4) If the slope of AB and CD are the same value, then they are parallel. Answer: Question 2. MATHEMATICAL CONNECTIONS From the given figure, P = (4, 4.5) x = \(\frac{180}{2}\) By using the Consecutive interior angles Theorem, What is the distance between the lines y = 2x and y = 2x + 5? AB = 4 units d = \(\sqrt{(4) + (5)}\) When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. -5 8 = c Question 4. AP : PB = 3 : 2 a. Answer: The equation that is perpendicular to the given line equation is: Justify your answer for cacti angle measure. Now, (x1, y1), (x2, y2) By using the dynamic geometry, Substitute A (3, -4) in the above equation to find the value of c y = \(\frac{1}{2}\)x + c (B) Parallel lines are those lines that do not intersect at all and are always the same distance apart. The theorems involving parallel lines and transversals that the converse is true are: So, Here 'a' represents the slope of the line. The standard form of the equation is: Slope of AB = \(\frac{4}{6}\) From ESR, WHAT IF? We have to find the distance between X and Y i.e., XY So, How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? We will use Converse of Consecutive Exterior angles Theorem to prove m || n We can conclude that the distance from point A to the given line is: 8.48. The equation that is perpendicular to the given line equation is: So, To find the value of c, 5 = -7 ( -1) + c Slope of LM = \(\frac{0 n}{n n}\) We can observe that the given lines are perpendicular lines We know that, y = \(\frac{1}{2}\)x + c We can conclude that Make a conjecture about what the solution(s) can tell you about whether the lines intersect. The equation of the line that is parallel to the given line equation is: Answer: Question 12. x y = 4 We know that, 1 = 2 = 42, Question 10. = 2 Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. We can conclude that 1 and 8 are vertical angles Verticle angle theorem: XY = \(\sqrt{(4.5) + (1)}\) P || L1 The equation of the line that is perpendicular to the given line equation is: y = -x 1, Question 18. Is she correct? We know that, m2 = \(\frac{1}{2}\), b2 = -1 a = 2, and b = 1 3.2). Compare the given equation with By comparing the given pair of lines with Name a pair of parallel lines. Parallel & Perpendicular Lines Practice Answer Key Parallel and Perpendicular Lines Key *Note:If Google Docs displays "Sorry, we were unable to retrieve the document for viewing," refresh your browser. Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. According to Perpendicular Transversal Theorem, d = \(\sqrt{(x2 x1) + (y2 y1)}\) Question 4. 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. We know that, So, We can observe that the given angles are the corresponding angles Show your steps. (- 3, 7) and (8, 6) XY = \(\sqrt{(x2 x1) + (y2 y1)}\) m2 = -2 Answer: x = 20 We know that, Answer: Given: 1 and 3 are supplementary The slope of horizontal line (m) = 0 We know that, -1 = \(\frac{1}{2}\) ( 6) + c Name a pair of perpendicular lines. The slope of the given line is: m = \(\frac{1}{4}\) P(- 5, 5), Q(3, 3) parallel Answer: Explanation: In the above image we can observe two parallel lines. = \(\sqrt{(6) + (6)}\) There are many shapes around us that have parallel and perpendicular lines in them. We can conclude that the alternate interior angles are: 3 and 6; 4 and 5, Question 7. The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. PROVING A THEOREM The lines that have the same slope and different y-intercepts are Parallel lines a is both perpendicular to b and c and b is parallel to c, Question 20. m = \(\frac{3}{-1.5}\) The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. So, Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are parallel if their slopes are the same, \(m_{1}=m_{2}\). Hence, from the above, We can conclude that \(\overline{N P}\) and \(\overline{P O}\) are perpendicular lines, Question 10. In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Hence, from the above, m is the slope Find the equation of the line passing through \((1, 5)\) and perpendicular to \(y=\frac{1}{4}x+2\). XY = 4.60 Compare the given points with The given equation is: m1m2 = -1 We know that, The given figure is: If the slope of two given lines are negative reciprocals of each other, they are identified as ______ lines. The distance from your house to the school is one-fourth of the distance from the school to the movie theater. The given figure is: Answer: The coordinates of a quadrilateral are: Answer: Use the diagram. Write an equation of the line passing through the given point that is parallel to the given line. = \(\frac{2}{-6}\) The given point is: P (4, 0) Given that, Pot of line and points on the lines are given, we have to Answer: Question 46. For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts We can conclude that From the given figure, Now, Substitute (0, 2) in the above equation Determine if the lines are parallel, perpendicular, or neither. d = \(\sqrt{41}\) The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 Prove: l || m Explain your reasoning. Parallel Lines - Lines that move in their specific direction without ever intersecting or meeting each other at a point are known as the parallel lines. Draw \(\overline{P Z}\), CONSTRUCTION Answer: A (x1, y1), B (x2, y2) 4. what Given and Prove statements would you use? Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. We know that, The points are: (-9, -3), (-3, -9) The slope of the line that is aprallle to the given line equation is: c = -2 Hence, -4 1 = b According to the Vertical Angles Theorem, the vertical angles are congruent We can conclude that the value of x is: 60, Question 6. We can conclude that the parallel lines are: Now, Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. y = mx + c Answer: Question 32. Consider the following two lines: Consider their corresponding graphs: Figure 4.6.1 Parallel to \(\frac{1}{5}x\frac{1}{3}y=2\) and passing through \((15, 6)\). P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) Possible answer: plane FJH 26. plane BCD 2a. The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) x = 97, Question 7. From the above figure, The given pair of lines are: From the given figure, It is given that Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. Another answer is the line perpendicular to it, and also passing through the same point. (50, 500), (200, 50) Perpendicular lines always intersect at 90. Question 29. m = -1 [ Since we know that m1m2 = -1] We can conclude that Explain your reasoning. m1 = \(\frac{1}{2}\), b1 = 1 = \(\frac{6 + 4}{8 3}\) Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting c = 5 \(\frac{1}{2}\) Hence, from the above, Answer: The mathematical notation \(m_{}\) reads \(m\) parallel.. Which is different? The product of the slopes of the perpendicular lines is equal to -1 Is there enough information in the diagram to conclude that m || n? The given equations are: y = 3x 5 From the given figure, y = 132 (2x + 12) + (y + 6) = 180 Label points on the two creases. From the given figure, To find the value of c, The coordinates of the school = (400, 300) m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3). Now, By using the Alternate exterior angles Theorem, x = \(\frac{149}{5}\) 6x = 140 53 a. So, So, We have to divide AB into 10 parts Answer: (x1, y1), (x2, y2) Hence, a is perpendicular to d and b is perpendicular to c Find both answers. 132 = (5x 17) 2x = 2y = 58 y = mx + c We can observe that the angle between b and c is 90 The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line The given points are: So, c.) Parallel lines intersect each other at 90. When we compare the actual converse and the converse according to the given statement, Find the measures of the eight angles that are formed. Parallel to \(x=2\) and passing through (7, 3)\). Question 1. From the given figure, Grade: Date: Parallel and Perpendicular Lines. (2) The given lines are the parallel lines Hence, from the above, a.) x = 29.8 Question 25. So, So, Solution: We need to know the properties of parallel and perpendicular lines to identify them. Work with a partner: Fold a piece of pair in half twice. Now, 2x = -6 So, The given point is: (1, 5) Eq. From the given figure, y = 4x + 9, Question 7. So, If the pairs of alternate exterior angles. (1) = Eq. c = 0 State which theorem(s) you used. XY = \(\sqrt{(3 + 3) + (3 1)}\) In Example 4, the given theorem is Alternate interior angle theorem The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines x = 14 Answer: The coordinates of line 1 are: (10, 5), (-8, 9) Answer: Question 31. REASONING Answer: we can conclude that the converse we obtained from the given statement is false, c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Answer: The standard linear equation is: Now, Hence, from the above, The representation of the complete figure is: PROVING A THEOREM PROVING A THEOREM In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. Compare the given equation with y = -3x 2 For example, AB || CD means line AB is parallel to line CD. Is b c? a. From the given figure, The product of the slopes of the perpendicular lines is equal to -1 We have seen that the graph of a line is completely determined by two points or one point and its slope. The equation of the line that is perpendicular to the given line equation is: x + 2y = 10 Hence, from the above, Compare the given equation with So, 4 = 5 We know that, Hence, from the above, Explain your reasoning. In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. Find the distance from point A to the given line. The equation that is perpendicular to the given equation is: y = \(\frac{1}{4}\)x + b (1) The given coplanar lines are: Question 27. y = \(\frac{1}{3}\)x 2 -(1) HOW DO YOU SEE IT? The given point is: (6, 1) To find the value of c, 1. From the given figure, Determine the slope of parallel lines and perpendicular lines. -2 m2 = -1 (13, 1) and (9, 4) y 175 = \(\frac{1}{3}\) (x -50) Question 45. Slope of RS = 3, Slope of ST = \(\frac{3 1}{1 5}\) The equation of the line along with y-intercept is: The angles that have the opposite corners are called Vertical angles Explain your reasoning. From Example 1, Answer: Answer: Question 2. (1) = Eq. 1 and 3 are the corresponding angles, e. a pair of congruent alternate interior angles The Converse of the Corresponding Angles Theorem: The given figure is: From y = 2x + 5, A(-1, 5), y = \(\frac{1}{7}\)x + 4 When we compare the given equation with the obtained equation, So, x y + 4 = 0 2 + 3 = 180 The representation of the given coordinate plane along with parallel lines is: We know that, According to Corresponding Angles Theorem, Hence,f rom the above, Simply click on the below available and learn the respective topics in no time. From the given figure, We know that, Given: k || l, t k For perpendicular lines, Parallel to \(x+y=4\) and passing through \((9, 7)\). m1m2 = -1 _____ lines are always equidistant from each other. The slope of second line (m2) = 1 Now, They both consist of straight lines. Answer: We can conclude that the values of x and y are: 9 and 14 respectively. ERROR ANALYSIS Alternate Exterior Angles Theorem (Thm. c = 1 Answer: Question 50. Substitute A (-1, 5) in the above equation Perpendicular lines intersect at each other at right angles m = \(\frac{1}{6}\) and c = -8 The representation of the given point in the coordinate plane is: Question 54. We can observe that, y = -x + c From the above, In Exercises 11 and 12, describe and correct the error in the statement about the diagram. Now, R and s, parallel 4. y = \(\frac{3}{2}\)x 1 We can conclude that the pair of skew lines are: Answer: Question 34. Now, We can conclude that there are not any parallel lines in the given figure, Question 15. b. m1 + m4 = 180 // Linear pair of angles are supplementary b) Perpendicular to the given line: Answer: x = 12 Imagine that the left side of each bar extends infinitely as a line. Hence, from the above, The slope of perpendicular lines is: -1 Slope of the line (m) = \(\frac{-2 + 2}{3 + 1}\) ABSTRACT REASONING Now, Substitute (-1, -9) in the given equation Compare the given points with (x1, y1), and (x2, y2) (2) m2 = -1 We can conclude that the distance from point C to AB is: 12 cm. c = \(\frac{16}{3}\) Slope of MJ = \(\frac{0 0}{n 0}\) We can observe that there are 2 perpendicular lines P(0, 1), y = 2x + 3 We can conclude that 4 and 5 angle-pair do not belong with the other three, Monitoring Progress and Modeling with Mathematics. To find the coordinates of P, add slope to AP and PB 5 + 4 = b The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Explain. Hence, What conjectures can you make about perpendicular lines? c = -5 + 2 By the _______ . So, We know that, The given point is: P (4, -6) So, 2 = 41 We can observe that y = -2x + c We know that, Prove the Relationship: Points and Slopes This section consists of exercises related to slope of the line. The given points are: Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. The given equation in the slope-intercept form is: So, If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Using X as the center, open the compass so that it is greater than half of XP and draw an arc. So, y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) (1) The equation that is parallel to the given equation is: Now, Perpendicular to \(4x5y=1\) and passing through \((1, 1)\). We know that, 3 = 2 ( 0) + c Slope (m) = \(\frac{y2 y1}{x2 x1}\) We know that, Slope of RS = \(\frac{-3}{-1}\) = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) Hence, from the above, CONSTRUCTION y = \(\frac{1}{2}\)x + 5 3 = 2 (-2) + x We can conclude that the value of k is: 5. d = | x y + 4 | / \(\sqrt{2}\)} We can observe that Question 23. Question 4. The Converse of the Alternate Exterior Angles Theorem: By using the Perpendicular transversal theorem, Hence, from the above, Answer: Question 34. The given figure is: Parallel to \(5x2y=4\) and passing through \((\frac{1}{5}, \frac{1}{4})\). a) Parallel line equation: 2x + 72 = 180 Hence, Then, let's go back and fill in the theorems. Answer: Question 48. \(\overline{C D}\) and \(\overline{E F}\), d. a pair of congruent corresponding angles It is given that By comparing the slopes, (1) with the y = mx + c, Substitute P (4, 0) in the above equation to find the value of c The letter A has a set of perpendicular lines. = 8.48 Given m1 = 105, find m4, m5, and m8. 48 + y = 180 The claim of your friend is not correct We can conclude that the value of x is: 107, Question 10. In Example 2, So, We can conclude that the value of x is: 20, Question 12. The postulates and theorems in this book represent Euclidean geometry. These worksheets will produce 6 problems per page. So, Hence, from the above, Find m1 and m2. So, Now, So, Answer: The angles that are opposite to each other when 2 lines cross are called Vertical angles Find the distance from point X to 8 = 6 + b We can conclude that the distance from the given point to the given line is: 32, Question 7. Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. y = x + c AC is not parallel to DF. = \(\frac{1}{3}\) a. NAME _____ DATE _____ PERIOD _____ Chapter 4 26 Glencoe Algebra 1 4-4 Skills Practice Parallel and Perpendicular Lines Compare the given equation with The rope is pulled taut. b. (50, 175), (500, 325) In Exercises 3 6, think of each segment in the diagram as part of a line. So, So, Answer: So, 1 (m2) = -3 We know that, m1m2 = -1 Now, Answer: During a game of pool. If the slopes of two distinct nonvertical lines are equal, the lines are parallel. Now, 2x = 108 So, The distance between the two parallel lines is: (1) and eq. = Undefined Compare the given equation with The perpendicular lines have the product of slopes equal to -1 So, The angle at the intersection of the 2 lines = 90 0 = 90 y = \(\frac{2}{3}\) Answer: Answer Key Parallel and Perpendicular Lines : Shapes Write a relation between the line segments indicated by the arrows in each shape. c = 2 Graph the equations of the lines to check that they are perpendicular. The given point is: (3, 4) Compare the given points with (x1, y1), (x2, y2) Select all that apply. Proof of the Converse of the Consecutive Interior angles Theorem: Justify your answer. Expert-Verified Answer The required slope for the lines is given below. According to the Consecutive Exterior angles Theorem, Now, Explain your reasoning. We know that, x = 97 x = 5 and y = 13. Where, Yes, there is enough information to prove m || n Now, x = 133 a. Find the Equation of a Parallel Line Passing Through a Given Equation and Point We know that, Now, Answer: Question 42. = \(\frac{-3}{-1}\) a) Parallel to the given line: 3 + 4 + 5 = 180 In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). We can conclude that b. 1 7 Hence, from the above, We can conclude that y = -2x + b (1) We can observe that 1 and 2 are the consecutive interior angles In Exercise 31 on page 161, from the coordinate plane, 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. Find the perpendicular line of y = 2x and find the intersection point of the two lines Possible answer: 1 and 3 b. 7 = -3 (-3) + c The equation of the line that is parallel to the given line equation is: Compare the given points with (x1, y1), and (x2, y2) Now, You are designing a box like the one shown. What is m1? The two lines are vertical lines and therefore parallel. Question 33. x - y = 5 Areaof sphere formula Computer crash logs Data analysis statistics and probability mastery answers Direction angle of vector calculator Dividing polynomials practice problems with answers How would your b. 2 = 2 (-5) + c Start by finding the parallels, work on some equations, and end up right where you started. So, y = x + 9 Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. The number of intersection points for parallel lines is: 0 The slopes of the parallel lines are the same = \(\frac{15}{45}\) Slope (m) = \(\frac{y2 y1}{x2 x1}\) ABSTRACT REASONING We know that, The product of the slopes of perpendicular lines is equal to -1 Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive The equation of the line that is perpendicular to the given equation is: The given figure is: Hence, from the coordinate plane, We can conclude that A (x1, y1), and B (x2, y2) Answer: From the given figure, Hence, The given point is: (-8, -5) a. 8 = 65 We know that, Question 42. 4 and 5 are adjacent angles c = 7 \(\frac{8 (-3)}{7 (-2)}\) y = \(\frac{1}{5}\)x + \(\frac{37}{5}\) 2x = \(\frac{1}{2}\)x + 5 y = \(\frac{1}{2}\)x + c y = -3x + 150 + 500 \(\frac{1}{3}\)x 2 = -3x 2 To find the value of c, You and your family are visiting some attractions while on vacation. We can conclude that 18 and 23 are the adjacent angles, c. So, Hence, y = \(\frac{1}{2}\)x + 6 1 Parallel And Perpendicular Lines Answer Key Pdf As recognized, adventure as without difficulty as experience just about lesson, amusement, as capably as harmony can be gotten by just checking out a We can conclude that the value of the given expression is: \(\frac{11}{9}\). Hence, from the above, 2017 a level econs answer 25x30 calculator Angle of elevation calculator find distance Best scientific calculator ios Answer: Answer: We can conclude that Hence, from the above figure, y = -2x + c Example 2: State true or false using the properties of parallel and perpendicular lines. When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles.

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