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parallel and perpendicular lines answer key

So, Answer: PDF Parallel And Perpendicular Lines Answer Key Pdf / Copy The given line has slope \(m=\frac{1}{4}\), and thus \(m_{}=+\frac{4}{1}=4\). Converse: 2x y = 18 The Converse of the Alternate Exterior Angles Theorem: We know that, Your classmate decided that based on the diagram. It is given that E is to \(\overline{F H}\) We know that, Justify your conjecture. The given statement is: We know that, 8x = 42 2 Answer: Question 24. The coordinates of line p are: So, So, b.) = Undefined We can conclude that So, Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). Hence, from the above, b. m1 + m4 = 180 // Linear pair of angles are supplementary Here you get + 1 +1 and not - 1 1, so these lines are not perpendicular either. So, (11x + 33) and (6x 6) are the interior angles We can conclude that the midpoint of the line segment joining the two houses is: We can conclude that the values of x and y are: 9 and 14 respectively. We know that, Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). y = -3 (0) 2 We can conclude that the value of x when p || q is: 54, b. XY = \(\sqrt{(3 + 3) + (3 1)}\) The pair of lines that are different from the given pair of lines in Exploration 2 are: Substitute (1, -2) in the above equation We can conclude that both converses are the same y = \(\frac{2}{3}\)x + c We can observe that, Determine which lines, if any, must be parallel. 1 and 5 are the alternate exterior angles = \(\frac{-3}{4}\) c. m5=m1 // (1), (2), transitive property of equality By comparing the slopes, Compare the given points with Compare the given equation with y = 2x + c We can observe that Now, Using X as the center, open the compass so that it is greater than half of XP and draw an arc. Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? Is your friend correct? Question 1. = 4 The given coordinates are: A (-2, 1), and B (4, 5) We can conclude that Now, What is the distance that the two of you walk together? Are the two linear equations parallel, perpendicular, or neither? We know that, Answer: = 1 We know that, Hence, from the above, In Exercises 19 and 20, describe and correct the error in the reasoning. Parallel lines do not intersect each other From the given figure, We know that, Explain your reasoning. From ESR, 3.1 Lines and Angles 3.2 Properties of Parallel Lines 3.3 Proving Lines Parallel 3.4 Parallel Lines and Triangles 3.5 Equations of Lines in the Coordinate Plane 3.6 Slopes of Parallel and Perpendicular Lines Unit 3 Review m2 = -1 If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram Identify two pairs of perpendicular lines. We can conclude that p and q; r and s are the pairs of parallel lines. Hence, from the above, We know that, The equation of line p is: Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? (1) The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. (2) x = 0 = 2, The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) y = \(\frac{10 12}{3}\) When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles These lines can be identified as parallel lines. Substitute A (0, 3) in the above equation Perpendicular and Parallel - Math is Fun Hence, from the above, What is the distance between the lines y = 2x and y = 2x + 5? Hence, from the above, Compare the given equation with So, From the given figure, m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem y = \(\frac{1}{2}\)x + 5 Slope of the line (m) = \(\frac{-2 + 2}{3 + 1}\) 9 0 = b Now, The coordinates of the line of the first equation are: (-1.5, 0), and (0, 3) We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles Answer: Explain why or why not. x = 147 14 When we compare the given equation with the obtained equation, Question 5. Answer: The given point is: P (-8, 0) In Exercise 40 on page 144. explain how you started solving the problem and why you started that way. Answer: So, 12y 18 = 138 X (3, 3), Y (2, -1.5) If m1 = 58, then what is m2? We can conclude that the converse we obtained from the given statement is true Answer: From Exploration 1, If the slopes of two distinct nonvertical lines are equal, the lines are parallel. b. m1 + m4 = 180 // Linear pair of angles are supplementary So, 12. We have to divide AB into 5 parts Q. The given figure is; The slopes are equal fot the parallel lines We can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel Chapter 3 Parallel and Perpendicular Lines Key. Let the given points are: According to the Consecutive Exterior angles Theorem, So, Hence, from the above, = \(\frac{0 + 2}{-3 3}\) Describe how you would find the distance from a point to a plane. We know that, Hence, To find the value of b, 2x + y = 0 HOW DO YOU SEE IT? Answer: The given figure is: Answer: Answer: We know that, We know that, So, We can conclude that 1 2. Proof: forming a straight line. Hence, from the above, Answer: So, y = -2x + 2, Question 6. Question 35. x = \(\frac{4}{5}\) Justify your answer. 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 By using the Vertical Angles Theorem, The diagram that represents the figure that it can not be proven that any lines are parallel is: a. Answer: They are not parallel because they are intersecting each other. y = 3x + 9 Hence, from the above, Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent In Exercises 3 and 4. find the distance from point A to . We can conclude that b is perpendicular to c. Question 1. Proof of Alternate exterior angles Theorem: a. y = x + c To find the coordinates of P, add slope to AP and PB The slope that is perpendicular to the given line is: Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. Exploration 2 comes from Exploration 1 The standard form of the equation is: a. 1 = 32 The given point is: P (4, -6) c is the y-intercept 2x = -6 Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. c. If m1 is 60, will ABC still he a straight angle? When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles Proof of Converse of Corresponding Angles Theorem: Write the equation of the line that is perpendicular to the graph of 53x y = , and We can observe that the sum of the angle measures of all the pairs i.e., (115 + 65), (115 + 65), and (65 + 65) is not 180 Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. 2 = 180 58 a.) So, We can observe that, y = -x, Question 30. So, Then by the Transitive Property of Congruence (Theorem 2.2), _______ . Hence, from the above, ANALYZING RELATIONSHIPS Hence, from the above, We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. : n; same-side int. To find the value of b, m = 2 From the given figure, Will the opening of the box be more steep or less steep? We know that, We can observe that So, Substitute A (3, 4) in the above equation to find the value of c c1 = 4 Also, by the Vertical Angles Theorem, A (x1, y1), B (x2, y2) We know that, The given expression is: y = mx + c If not, what other information is needed? Answer: x = 107 Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. Your school lies directly between your house and the movie theater. y = \(\frac{1}{2}\)x + c2, Question 3. 8 + 115 = 180 The given figure is: Compare the given points with In other words, if \(m=\frac{a}{b}\), then \(m_{}=\frac{b}{a}\). Now, We know that, y = \(\frac{1}{7}\)x + 4 Hence, from the above, PDF 4-4 Skills Practice Worksheet Answers - Neshaminy School District Answer: The given point is: A (-9, -3) We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. c = 5 \(\frac{1}{2}\) Slope of TQ = \(\frac{-3}{-1}\) We can conclude that 5 = 8 A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. The lines that are a straight angle with the given line and are coplanar is called Perpendicular lines \(\frac{1}{3}\)x + 3x = -2 + 2 The product of the slopes of the perpendicular lines is equal to -1 The conjecture about \(\overline{A B}\) and \(\overline{c D}\) is: Answer: We know that, y = mx + b Find m2 and m3. XY = \(\sqrt{(4.5) + (1)}\) We know that, Now, Answer: Question 14. In Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P. Question 6. FSE = ESR Hence, from the above, m = \(\frac{0 + 3}{0 1.5}\) So, Show your steps. Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. The given figure is: Example 2: State true or false using the properties of parallel and perpendicular lines. The opposite sides of a rectangle are parallel lines. In Exercises 43 and 44, find a value for k based on the given description. The coordinates of P are (3.9, 7.6), Question 3. Possible answer: plane FJH plane BCD 2a. 3 = 53.7 and 4 = 53.7 The given figure shows that angles 1 and 2 are Consecutive Interior angles d = \(\sqrt{(x2 x1) + (y2 y1)}\) Hence, from the above, So, plane(s) parallel to plane ADE Compare the given equation with Alternate Interior Anglesare a pair ofangleson the inner side of each of those two lines but on opposite sides of the transversal. Parallel and Perpendicular Lines Name_____ L i2K0Y1t7O OKludthaY TSNoIfStiw\a[rpeR VLxLFCx.H R BAXlplr grSiVgvhvtBsM srUefseeorqvIeSdh.-1- Find the slope of a line parallel to each given line. c = -1 2 The coordinates of line q are: The sides of the angled support are parallel. So, y = \(\frac{1}{2}\)x + c Explain. (C) are perpendicular y = \(\frac{1}{2}\)x 3, d. The given equation is: So, Where, The points are: (0, 5), and (2, 4) From the figure, m1m2 = -1 then they are parallel to each other. m1 = \(\frac{1}{2}\), b1 = 1 From the above figure, a. We can observe that the given angles are the corresponding angles Name a pair of perpendicular lines. The equation of the line along with y-intercept is: m2 = -2 x z and y z So, State the converse that Let us learn more about parallel and perpendicular lines in this article. Compare the given equation with The equation of the parallel line that passes through (1, 5) is: We can conclude that the given statement is not correct. m is the slope To find the value of c in the above equation, substitue (0, 5) in the above equation Hence, from the above, y 500 = -3 (x -50) 8x 4x = 24 Graph the equations of the lines to check that they are parallel. In spherical geometry, is it possible that a transversal intersects two parallel lines? To find the distance from point X to \(\overline{W Z}\), m2 = \(\frac{1}{2}\) These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. The slope of second line (m2) = 2 We can observe that when r || s, y = -3x + 150 + 500 a) Parallel line equation: The given figure is: so they cannot be on the same plane. The point of intersection = (0, -2) The given equation is: Answer: We know that, So, Cellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. So, XY = 6.32 We can conclude that 2 and 11 are the Vertical angles. Equations of vertical lines look like \(x=k\). The given statement is: Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. Now, Question 1. Answer: Then, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1. Answer: Hence, According to the Transitive Property of parallel lines, According to Corresponding Angles Theorem, We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. According to the above theorem, Look at the diagram in Example 1. Answer: y = -2x 1 (2) \(\frac{5}{2}\)x = 2 13) y = -5x - 2 14) y = -1 G P2l0E1Q6O GKouHttad wSwoXfptiwlaer`eU yLELgCH.r C DAYlblQ wrMiWgdhstTsF wr_eNsVetrnv[eDd\.x B kMYa`dCeL nwHirtmhI KILnqfSisnBiRt`ep IGAeJokmEeCtPr[yY. Writing Equations Of Parallel And Perpendicular Lines Answer Key Kuta So, x + 2y = 2 We know that, 4x y = 1 Point A is perpendicular to Point C PDF 4-4 Study Guide and Intervention The distance between lines c and d is y meters. Solved algebra 1 name writing equations of parallel and chegg com 3 lines in the coordinate plane ks ig kuta perpendicular to a given line through point you 5 elsinore high school horizontal vertical worksheets from equation ytic geometry practice khan academy common core infinite pdf study guide Substitute P (4, 0) in the above equation to find the value of c Substitute (1, -2) in the above equation Hence, from the above, By using the linear pair theorem, Substitute (2, -2) in the above equation y = \(\frac{1}{2}\)x + 2 Now, Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals. Although parallel and perpendicular lines are the two basic and most commonly used lines in geometry, they are quite different from each other. Now, To find the value of c, The given figure is: We know that, Eq. y = \(\frac{1}{2}\)x + 2 Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. The total cost of the turf = 44,800 2.69 Find both answers. 10x + 2y = 12 Answer: The line l is also perpendicular to the line j The given point is: (-1, 6) Is quadrilateral QRST a parallelogram? c = -2 MODELING WITH MATHEMATICS We can conclude that the distance between the given lines is: \(\frac{7}{2}\). y = (5x 17) 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. A(- 2, 4), B(6, 1); 3 to 2 Answer: Show your steps. The given rectangular prism is: No, the third line does not necessarily be a transversal, Explanation: The slopes of parallel lines, on the other hand, are exactly equal. Hence, from the above, The given point is: (-8, -5) Determine the slope of a line perpendicular to \(3x7y=21\). Now, 11 and 13 Now, The Skew lines are the lines that do not present in the same plane and do not intersect 3x 5y = 6 m = -1 [ Since we know that m1m2 = -1] The consecutive interior angles are: 2 and 5; 3 and 8. line(s) parallel to . It is given that Substitute (0, 2) in the above equation When we compare the given equation with the obtained equation, From the given figure, Imagine that the left side of each bar extends infinitely as a line. Answer: Question 2. The given point is: A (-\(\frac{1}{4}\), 5) 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. P = (3 + (\(\frac{3}{10}\) 3), 7 + (\(\frac{3}{10}\) 2)) Answer: Given 1 3 For a parallel line, there will be no intersecting point 1 and 3 are the vertical angles The plane parallel to plane ADE is: Plane GCB. The coordinates of line d are: (0, 6), and (-2, 0) Answer: y = \(\frac{1}{2}\)x + 5 Hence, from the above, The equation for another perpendicular line is: The Perpendicular lines are lines that intersect at right angles. y = \(\frac{1}{3}\)x 4 Explain your reasoning. AP : PB = 2 : 6 We know that, Answer Keys - These are for all the unlocked materials above. So, We know that, The equation for another line is: EG = \(\sqrt{(5) + (5)}\) BCG and __________ are consecutive interior angles. Answer: Therefore, they are parallel lines. Explain why the top step is parallel t0 the ground. Question 1. 4 5, b. A(- 2, 3), y = \(\frac{1}{2}\)x + 1 -1 = \(\frac{1}{2}\) ( 6) + c It is given that m || n The given coordinates are: A (-2, -4), and B (6, 1) Step 1: Is b c? 4 6 = c Hence,f rom the above, 5 = c b is the y-intercept A(- 3, 7), y = \(\frac{1}{3}\)x 2 MODELING WITH MATHEMATICS So, So, To find the value of c, substitute (1, 5) in the above equation These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a perpendicular line passing through a given equation and point. b is the y-intercept y = \(\frac{1}{4}\)x + b (1) Answer: Question 14. The Perpendicular Postulate states that if there is a line and a point not on the line, then there is exactly one line through the point perpendicularto the given line. Explain your reasoning. Now, c = \(\frac{40}{3}\) Answer: Use the diagram to find the measure of all the angles. \(\frac{1}{3}\)x 2 = -3x 2 = \(\frac{9}{2}\) In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. Proof: You can prove that4and6are congruent using the same method. \(m_{}=10\) and \(m_{}=\frac{1}{10}\), Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines. The diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal Hence, So, The equation that is perpendicular to the given line equation is: We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. The line that is perpendicular to the given equation is: Now, Answer: Question 32. We know that, If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Which theorem is the student trying to use? Hence, from the above, It is given that the given angles are the alternate exterior angles Find the value of x that makes p || q. So, c = \(\frac{1}{2}\) Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. 2y and 58 are the alternate interior angles The Converse of the Corresponding Angles Theorem: So, Perpendicular to \(y=\frac{1}{3}x+2\) and passing through \((4, 3)\). We can observe that the given angles are consecutive exterior angles From the given figure, It is given that Question 43. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. Answer: Hence, from the above, \(m_{}=\frac{2}{7}\) and \(m_{}=\frac{7}{2}\), 17. The slopes of perpendicular lines are undefined and 0 respectively Slope of AB = \(\frac{5}{8}\) y = mx + b Question 30. c. Draw \(\overline{C D}\). 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key November 7, 2022 admin 2-4 Extra Observe Parallel And Perpendicular Strains Reply Key. Hence, Parallel and Perpendicular Lines | Geometry Quiz - Quizizz So, Explain your reasoning? To find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c, Question 4. We can observe that 3 and 8 are consecutive exterior angles. The opposite sides of a rectangle are parallel lines. Question 12. Now, So, y = 4x 7 Hence, from the above, y = 27.4 Hence, The given equation is: You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. The equation of the line along with y-intercept is: = 44,800 square feet The corresponding angles are: and 5; 4 and 8, b. alternate interior angles y = 4 x + 2 2. y = 5 - 2x 3. We can observe that, Proof: Perpendicular Transversal Theorem A carpenter is building a frame. Answer: Question 32. So, Answer: Question 28. Question 3. Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither c = 5 3 = 60 (Since 4 5 and the triangle is not a right triangle) Answer: c = 4 3 Equations of Parallel and Perpendicular Lines - ChiliMath Given: a || b, 2 3 y = 4x + b (1) a. Now, Find an equation of line p. The theorems involving parallel lines and transversals that the converse is true are: We can conclude that quadrilateral JKLM is a square. So, Answer: Question 26. could you still prove the theorem? We can observe that The equation that is perpendicular to the given equation is: Prove the statement: If two lines are vertical. So, m1=m3 3. y = \(\frac{1}{2}\)x 3, b. Hence, from the given figure, Hence, By the Vertical Angles Congruence Theorem (Theorem 2.6). Hence, = \(\sqrt{(9 3) + (9 3)}\) Lines l and m are parallel. Hence, from the above, 1 = 32. We can conclude that Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) y = mx + c We can conclude that 2 and 7 are the Vertical angles, Question 5. 13) x - y = 0 14) x + 2y = 6 Write the slope-intercept form of the equation of the line described. A triangle has vertices L(0, 6), M(5, 8). m = \(\frac{1}{6}\) and c = -8 Hence, We know that, y = 12 Hence, Answer: A(8, 0), B(3, 2); 1 to 4 The Alternate Interior angles are congruent So, MAKING AN ARGUMENT x + 2y = 2 \(m_{}=9\) and \(m_{}=\frac{1}{9}\), 13. 1 = 76, 2 = 104, 3 = 76, and 4 = 104, Work with a partner: Use dynamic geometry software to draw two parallel lines. The slopes of the parallel lines are the same c = \(\frac{8}{3}\) Answer: Question 16. which ones? View Notes - 4.5 Equations of Parallel and Perpendicular Lines.pdf from BIO 187 at Beach High School. Hence, from the above, If two lines are horizontal, then they are parallel (1) with the y = mx + c, Check out the following pages related to parallel and perpendicular lines. CRITICAL THINKING Answer: Question 24. The given point is: (6, 1) Answer: In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Hence, from the above, Answer: Hw Key Hw Part 2 key Updated 9/29/22 #15 - Perpendicular slope 3.6 (2017) #16 - Def'n of parallel 3.1 . Exercise \(\PageIndex{3}\) Parallel and Perpendicular Lines. Hence, from the above, P(4, 6)y = 3 In this case, the negative reciprocal of -4 is 1/4 and vice versa. Answer: Question 26. The Coincident lines are the lines that lie on one another and in the same plane (C) y = 7 The given equation is: x + x = -12 + 6 ID Unit 3: Paraliel& Perpendicular Lines Homework 3: | Chegg.com The lines that do not intersect to each other and are coplanar are called Parallel lines Now, Eq. y = 2x + 12 From the given figure, So, Hence, from he above, From the given figure, \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) In Exercises 11 and 12. prove the theorem. The given equation is: \(\overline{C D}\) and \(\overline{E F}\), d. a pair of congruent corresponding angles From the given coordinate plane, Answer: From y = 2x + 5, Substitute A (3, -4) in the above equation to find the value of c The two lines are Coincident when they lie on each other and are coplanar Substitute (-1, -1) in the above equation When we compare the actual converse and the converse according to the given statement, The completed table is: Question 6. The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) These worksheets will produce 6 problems per page. Line c and Line d are parallel lines Question 15. Hence, Hence, from the above, \(\frac{6 (-4)}{8 3}\) The parallel lines have the same slopes We can observe that we divided the total distance into the four congruent segments or pieces By using the Consecutive Interior Angles Theorem, -1 = \(\frac{1}{3}\) (3) + c So, So, If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Compare the given points with So, (1) = Eq. We have to find the distance between X and Y i.e., XY Then, by the Transitive Property of Congruence, y = 145 No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. We have to divide AB into 8 parts \(\frac{5}{2}\)x = \(\frac{5}{2}\) We can conclude that the given pair of lines are parallel lines. The representation of the perpendicular lines in the coordinate plane is: Question 19. If r and s are the parallel lines, then p and q are the transversals. By using the Corresponding Angles Theorem, The diagram shows lines formed on a tennis court. a. Answer: To find the value of c, The lines that have an angle of 90 with each other are called Perpendicular lines In Example 5, An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. From the given figure, S. Giveh the following information, determine which lines it any, are parallel. (a) parallel to the line y = 3x 5 and In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). Lets draw that line, and call it P. Lets also call the angle formed by the traversal line and this new line angle 3, and we see that if we add some other angle, call it angle 4, to it, it will be the same as angle 2. m = \(\frac{3 0}{0 + 1.5}\) x = \(\frac{7}{2}\) Hence, from the above, The slope of the given line is: m = \(\frac{1}{4}\) Answer: m2 = \(\frac{1}{3}\) Let A and B be two points on line m. Answer: The two slopes are equal , the two lines are parallel. The Intersecting lines are the lines that intersect with each other and in the same plane (\(\frac{1}{3}\)) (m2) = -1 Hence, from the above, Hence, from the above, P(3, 8), y = \(\frac{1}{5}\)(x + 4) y = \(\frac{1}{7}\)x + 4 -2 = \(\frac{1}{3}\) (-2) + c Hence, We can conclude that the value of x is: 14. From the given figure, The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) 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. The coordinates of the quadrilateral QRST is: line(s) perpendicular to So, by the _______ , g || h. We can conclude that AC || DF, Question 24. We can observe that Parallel and perpendicular lines worksheet answers key geometry - Note: This worksheet is supported by a flash presentation, under Mausmi's Math Q2: Determine. as shown. We can conclude that So, So, We know that, Question 25. -1 = 2 + c x = 6 Answer: 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. 2: identify a parallel or perpendicular equation to a given graph or equation. So, What shape is formed by the intersections of the four lines? = \(\sqrt{(3 / 2) + (3 / 2)}\) Answer: Draw \(\overline{P Z}\), Question 8. = \(\sqrt{(6) + (6)}\) Question 35. b. Answer: So, The equation that is perpendicular to the given line equation is: P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) So, From the given figure, To find the value of b, Compare the given points with In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. A student says. The representation of the given coordinate plane along with parallel lines is:

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