parallel and perpendicular lines answer key

For which of the theorems involving parallel lines and transversals is the converse true? 8 + 115 = 180 Now, Identifying Parallel, Perpendicular, and Intersecting Lines from a Graph 3.2). The given points are: A(- 2, 3), y = $\frac{1}{2}$x + 1 We can conclude that 8 right angles are formed by two perpendicular lines in spherical geometry. 3x 2x = 20 m = $\frac{0 + 3}{0 1.5}$ 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. The equation that is parallel to the given equation is: P(0, 1), y = 2x + 3 1 + 57 = 180 We can observe that the given lines are parallel lines 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. Compare the given equation with To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. Answer: Unit 3 Parallel And Perpendicular Lines Homework 4 Answer Key From the coordinate plane, Find the perpendicular line of y = 2x and find the intersection point of the two lines The points are: (-9, -3), (-3, -9) { "3.01:_Rectangular_Coordinate_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.02:_Graph_by_Plotting_Points" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.03:_Graph_Using_Intercepts" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.04:_Graph_Using_the_y-Intercept_and_Slope" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.05:_Finding_Linear_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.06:_Parallel_and_Perpendicular_Lines" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.07:_Introduction_to_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.08:_Linear_Inequalities_(Two_Variables)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.0E:_3.E:_Review_Exercises_and_Sample_Exam" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Real_Numbers_and_Their_Operations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Linear_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Graphing_Lines" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Solving_Linear_Systems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Polynomials_and_Their_Operations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Factoring_and_Solving_by_Factoring" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Rational_Expressions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Radical_Expressions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Solving_Quadratic_Equations_and_Graphing_Parabolas" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Appendix_-_Geometric_Figures" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbyncsa", "showtoc:no", "authorname:anonymous", "licenseversion:30", "program:hidden" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FAlgebra%2FBeginning_Algebra%2F03%253A_Graphing_Lines%2F3.06%253A_Parallel_and_Perpendicular_Lines, $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}$ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$, Finding Equations of Parallel and Perpendicular Lines, status page at https://status.libretexts.org. Name them. In Exercises 11 and 12. prove the theorem. We know that, Which angle pair does not belong with the other three? The slopes are the same and the y-intercepts are different The given equation is: Hence, from the above, Substitute (1, -2) in the above equation m2 and m4 = $\frac{2}{9}$ Answer: Hence, Describe and correct the error in the students reasoning MAKING AN ARGUMENT Justify your conclusion. We have to find the point of intersection Answer: From the given coordinate plane, Let the given points are: A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) We know that, Slope of the line (m) = \frac {y2 - y1} {x2 - x1} So, c. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. 3. Answer: Question 20. 2 and 3 Which rays are parallel? So, Answer: Question 2. 1 = 0 + c The coordinates of x are the same. We know that, EG = $\sqrt{(5) + (5)}$ Answer: Parallel to $y=\frac{3}{4}x3$ and passing through $(8, 2)$. The equation of the line along with y-intercept is: Hence, From the given figure, Select all that apply. The slope of the given line is: m = 4 The slope of the given line is: m = $\frac{2}{3}$ Art and Culture: Abstract Art: Lines, Rays, and Angles - Saskia Lacey 2017-09-01 Students will develop their geometry skills as they study the geometric shapes of modern art and read about the . The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior anglesof two lines crossed by a transversal are congruent, then the two lines are parallel. It is given that m || n b.) = 9.48 The midpoint of PQ = ($\frac{x1 + x2}{2}$, $\frac{y1 + y2}{2}$) Hence, The coordinates of P are (3.9, 7.6), Question 3. Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. So, Compare the given points with So, = $\frac{-4}{-2}$ y = $\frac{2}{3}$x + 1 Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. Hence, from the above, We can conclude that Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. Look at the diagram in Example 1. Now, The slope of the line of the first equation is: Hence, from the above figure, Given m1 = 115, m2 = 65 Two lines are termed as parallel if they lie in the same plane, are the same distance apart, and never meet each other. Enter a statement or reason in each blank to complete the two-column proof. 3.6: Parallel and Perpendicular Lines - Mathematics LibreTexts To find the value of b, (2x + 20)= 3x The slopes are equal fot the parallel lines y = 2x and y = 2x + 5 Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. The given point is: A (3, -4) The diagram that represents the figure that it can not be proven that any lines are parallel is: Hence, from the above, We can observe that 141 and 39 are the consecutive interior angles y = $\frac{3}{2}$x 1 Identify two pairs of parallel lines so that each pair is in a different plane. From the given figure, We can observe that the slopes are the same and the y-intercepts are different y = mx + c x + 2y = 2 So, Hence, from the above figure, The given figure is: Question 27. 1 = 123 Spectrum Math Grade 4 Chapter 8 Lesson 2 Answer Key Parallel and Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. By using the linear pair theorem, We know that, We can conclude that the distance between the lines y = 2x and y = 2x + 5 is: 2.23. The coordinates of the subway are: (500, 300) Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3). XY = $\sqrt{(x2 x1) + (y2 y1)}$ We know that, We know that, Geometry chapter 3 parallel and perpendicular lines answer key - Math 17x = 180 27 We know that, $\frac{1}{3}$x 2 = -3x 2 So, Justify your answers. Explain your reasoning. x = 9. A(8, 2),y = 4x 7 The lines that do not intersect to each other and are coplanar are called Parallel lines m2 = $\frac{1}{2}$, b2 = 1 Answer: Question 46. Question 31. Geometry parallel and perpendicular lines answer key In Exercise 40 on page 144, You meet at the halfway point between your houses first and then walk to school. 1 = 41 The representation of the given coordinate plane along with parallel lines is: PDF ANSWERS a. So, You and your family are visiting some attractions while on vacation. Find the distance from the point (- 1, 6) to the line y = 2x. Answer: It is given that Explain your reasoning. 2x = 7 Name a pair of perpendicular lines. A (x1, y1), and B (x2, y2) Question 1. So, Now, m1m2 = -1 Given that, Pot of line and points on the lines are given, we have to In the parallel lines, Line 2: (2, 1), (8, 4) So, y = mx + c y = -2x 1 (2) a. 68 + (2x + 4) = 180 $\frac{8 (-3)}{7 (-2)}$ Hence, from the above, So, Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. We have to find the point of intersection y = 27.4 Now, 6x = 140 53 It is given that Step 1: Find the slope $m$. = 2 (2) The given figure is: A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. 1 + 2 = 180 It is given that a student claimed that j K, j l Hence, from the above, 2 = 123 Perpendicular to $\frac{1}{2}x\frac{1}{3}y=1$ and passing through $(10, 3)$. x = $\frac{24}{4}$ Hence, from the above, c = 2 This page titled 3.6: Parallel and Perpendicular Lines is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Anonymous. Justify your answer. then they are supplementary. The Converse of Corresponding Angles Theorem: From the given figure, Now, XY = $\sqrt{(3 + 3) + (3 1)}$ y = 145 m2 = -2 Classify the pairs of lines as parallel, intersecting, coincident, or skew. So, We can conclude that the equation of the line that is parallel to the line representing railway tracks is: $\begin{array}{cc} {\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(-1,-5)}&{m_{\perp}=4}\end{array}$. x z and y z -3 = -2 (2) + c Part - A Part - B Sheet 1 5) 6) Identify the pair of parallel and perpendicular line segments in each shape. When we compare the given equation with the obtained equation, The given point is: A(3, 6) From the given figure, d = | 6 4 + 4 |/ $\sqrt{2}$} y = $\frac{1}{5}$x + c Proof of the Converse of the Consecutive Interior angles Theorem: We can conclude that the third line does not need to be a transversal. So, m1m2 = -1 We can conclude that the converse we obtained from the given statement is true Write the converse of the conditional statement. y = $\frac{1}{5}$x + $\frac{4}{5}$ Now, The given point is: P (-8, 0) AB = 4 units We know that, Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. Answer: So, Lines Perpendicular to a Transversal Theorem (Thm. The equation for another line is: MATHEMATICAL CONNECTIONS Hence, Perpendicular to $y=3x1$ and passing through $(3, 2)$. We know that, Answer: Hence, from the above, Hence, from the above, (5y 21) = 116 Parallel and perpendicular lines worksheet answers key geometry - Note: This worksheet is supported by a flash presentation, under Mausmi's Math Q2: Determine. 2x + y = 162(1) m1 and m5 A(- $\frac{1}{4}$, 5), x + 2y = 14 So, Question 5. Now, Are the markings on the diagram enough to conclude that any lines are parallel? 3 + 4 = c We can observe that the given pairs of angles are consecutive interior angles She says one is higher than the other. = 2.23 From the given figure, We can conclude that The given figure is: 2x = 108 A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. So, by the Corresponding Angles Converse, g || h. Question 5. Slope (m) = $\frac{y2 y1}{x2 x1}$ Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). So, = $\frac{-3}{-1}$ $\frac{1}{2}$ . The given equation is: In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. 2 = 150 (By using the Alternate exterior angles theorem) Lines that are parallel to each other will never intersect. From the given figure, y 500 = -3 (x -50) We can conclude that the slope of the given line is: 0. Slope (m) = $\frac{y2 y1}{x2 x1}$ Answer: Writing Equations Of Parallel And Perpendicular Lines Answer Key Kuta = $\frac{-6}{-2}$ Answer: Answer: Question 30. Vertical and horizontal lines are perpendicular. Answer: We can observe that, We have to divide AB into 5 parts Answer: Question 2. We know that, y = $\frac{10 12}{3}$ The given point is: (4, -5) We can conclude that the claim of your classmate is correct. From the given figure, c = 3 4 Answer: A(2, 0), y = 3x 5 Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. The given points are: So, Hence, from the above, Answer: We can conclude that We can conclue that Find the measure of the missing angles by using transparent paper. Answer: m2 = -1 The angles are (y + 7) and (3y 17) So, We know that, m2 = $\frac{1}{2}$ So, Answer: Alternate Exterior Angles Theorem (Thm. We can observe that In the same way, when we observe the floor from any step, Answer: A(1, 6), B(- 2, 3); 5 to 1 2 + 10 = c Question 1. c = -9 3 We can conclude that m || n, Question 15. So, Question 20. The given lines are perpendicular lines In Example 5. yellow light leaves a drop at an angle of m2 = 41. Explain our reasoning. Show your steps. In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. m1m2 = -1 We know that, Name two pairs of congruent angles when $\overline{A D}$ and $\overline{B C}$ are parallel? We can conclude that the distance between the given lines is: $\frac{7}{2}$. Answer: 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. Now, y = $\frac{2}{3}$ = 2.12 Given a b To find the value of c, 3m2 = -1 (- 3, 7) and (8, 6) Use the Distance Formula to find the distance between the two points. such as , are perpendicular to the plane containing the floor of the treehouse. A(3, 4), y = x So, Answer: Question 23. The given points are: P (-7, 0), Q (1, 8) So, ax + by + c = 0 m2 = $\frac{1}{2}$ We can observe that 1 and 4; 2 and 3 are the pairs of corresponding angles Hence, from the above, 12. x = 147 14 E (x1, y1), G (x2, y2) Which line(s) or plane(s) appear to fit the description? The two pairs of perpendicular lines are l and n, c. Identify two pairs of skew line The given point is: (-3, 8) So, No, there is no enough information to prove m || n, Question 18. m = 2 Question 4. Answer: m2 = 3 Use the numbers and symbols to create the equation of a line in slope-intercept form Equations of vertical lines look like $x=k$. 1) y = -3x 2 = $\frac{3}{4}$ Answer: From the above, y = 3x + c Answer: 1 4. Now, P(0, 0), y = 9x 1 We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: 2 and 7 are vertical angles MODELING WITH MATHEMATICS Corresponding Angles Theorem The points of intersection of parallel lines: x = y =29 The conjecture about $\overline{A B}$ and $\overline{c D}$ is: = $\frac{-1}{3}$ Look back at your construction of a square in Exercise 29 on page 154. Question 9. We can conclude that In spherical geometry, all points are points on the surface of a sphere. Each rung of the ladder is parallel to the rung directly above it. 7 = -3 (-3) + c so they cannot be on the same plane. = 255 yards We can conclude that So, So, So, The lines that do not intersect and are not parallel and are not coplanar are Skew lines The equation of the line that is parallel to the given line equation is: (x1, y1), (x2, y2) Hence, y = $\frac{1}{2}$x 3 If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. a = 1, and b = -1 y = 3x + 9 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. We know that, For parallel lines, Substitute (-5, 2) in the given equation 5 = 8 Hence, Find the slope of the line perpendicular to $15x+5y=20$. Use a graphing calculator to graph the pair of lines. Hence, Answer: A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). We can conclude that the distance that the two of the friends walk together is: 255 yards. Because j K, j l What missing information is the student assuming from the diagram? We can conclude that FCA and JCB are alternate exterior angles. We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. V = (-2, 3) The distance between the perpendicular points is the shortest Now, E (-4, -3), G (1, 2) The given parallel line equations are: Alternate Interior angles theorem: The product of the slopes of the perpendicular lines is equal to -1 The given statement is: We can conclude that the vertical angles are: Hence, Answer: The given statement is: Answer: Find the slope of each line. When we compare the given equation with the obtained equation, The third intersecting line can intersect at the same point that the two lines have intersected as shown below: To be proficient in math, you need to analyze relationships mathematically to draw conclusions. The equation of the line that is parallel to the given equation is: Hence, from the above, x + 2y = 2 We can conclude that m1 m2 = $\frac{1}{2}$ 2 We can conclude that 3 = 76 and 4 = 104 The equation that is perpendicular to the given equation is: Answer: The given figure is: Slope of the line (m) = $\frac{-1 2}{-3 + 2}$ Proof: Hence, from the above, m2 = -3 To find the value of c in the above equation, substitue (0, 5) in the above equation Answer: The given points are A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) m = Substitute A (-1, 2), and B (3, -1) in the formula. 3x = 69 9+ parallel and perpendicular lines maze answer key pdf most standard We can observe that there are 2 pairs of skew lines We can conclude that Your school has a $1,50,000 budget. Use the diagram. The given figure is: From the given figure, The given figure is: Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Slope (m) = $\frac{y2 y1}{x2 x1}$ Compare the given equations with w y and z x = 1.67 The equation that is perpendicular to the given line equation is: 2. We know that, The standard form of the equation is: Horizontal and vertical lines are perpendicular to each other. b) Perpendicular to the given line: We know that, lines intersect at 90. Intersecting lines can intersect at any . Compare the given points with We know that, Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines Hence, from the above, The bottom step is parallel to the ground. Slope of AB = $\frac{5 1}{4 + 2}$ Answer: The given line equation is: Answer the questions related to the road map. (180 x) = x We know that, We know that, = ($\frac{8 + 0}{2}$, $\frac{-7 + 1}{2}$) Find the equation of the line passing through $(\frac{7}{2}, 1)$ and parallel to $2x+14y=7$. We have to find the distance between A and Y i.e., AY Answer: Question 26. Now, We can conclude that the given statement is not correct. $\overline{C D}$ and $\overline{A E}$ Answer: Question 48. m2 = -1 In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. If the line cut by a transversal is parallel, then the corresponding angles are congruent We know that, THINK AND DISCUSS, PAGE 148 1. Compare the given equation with 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 -5 = 2 (4) + c Answer: Question 28. Now, Now, It is given that The given figure is: Answer: Question 14. The equation of the line along with y-intercept is: Now, Now, .And Why To write an equation that models part of a leaded glass window, as in Example 6 3-7 11 Slope and Parallel Lines Key Concepts Summary Slopes of Parallel Lines If two nonvertical lines are parallel, their slopes are equal. Exercise $\PageIndex{3}$ Parallel and Perpendicular Lines. Answer: The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar We can conclude that the alternate interior angles are: 3 and 6; 4 and 5, Question 7. The rungs are not intersecting at any point i.e., they have different points Hence, from the above, Perpendicular to $x=\frac{1}{5}$ and passing through $(5, 3)$. 2 = 180 123 b. We can conclude that Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent c = 1 We have to find the point of intersection The length of the field = | 20 340 | m1m2 = -1 P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) When we compare the actual converse and the converse according to the given statement, We can conclude that the value of x is: 90, Question 8. Hence, from the above, 3 = 68 and 8 = (2x + 4) So, XY = 6.32 We can conclude that your friend is not correct. = $\frac{11}{9}$ y = $\frac{1}{2}$x $\frac{1}{2}$, Question 10. The lines that do not intersect or not parallel and non-coplanar are called Skew lines We get They are not perpendicular because they are not intersecting at 90. For parallel lines, Question 1. The postulates and theorems in this book represent Euclidean geometry. y = mx + c According to the Perpendicular Transversal Theorem, A(- 2, 4), B(6, 1); 3 to 2 In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. We know that, We can conclude that the pair of parallel lines are: Hence, from the above, Explain Your reasoning. alternate exterior The map shows part of Denser, Colorado, Use the markings on the map. The given figure is: REASONING According to Corresponding Angles Theorem, Answer: There is not any intersection between a and b We can observe that MATHEMATICAL CONNECTIONS So, Label the intersection as Z. y = $\frac{3}{2}$x + 2 Prove that horizontal lines are perpendicular to vertical lines. We can conclude that the perpendicular lines are: c = 1 We know that, From Exploration 2, Graph the equations of the lines to check that they are parallel. y = $\frac{1}{3}$x + c We know that, 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 2x + $\frac{1}{2}$x = 5 ABSTRACT REASONING Hence those two lines are called as parallel lines. Answer: We know that, y = mx + b 1 (m2) = -3 Which pair of angle measures does not belong with the other three? The slopes are equal fot the parallel lines Converse: Question 1. The given point is: (6, 1) We can conclude that the given lines are parallel. The equation of line p is: Substitute A (3, 4) in the above equation to find the value of c XY = $\sqrt{(6) + (2)}$ y = -2 The given point is: (1, 5) corresponding = $\frac{6 + 4}{8 3}$ So, Answer: = $\frac{8 0}{1 + 7}$ Step 3: Name the line(s) through point F that appear skew to . Answer: Question 2. y = $\frac{1}{7}$x + 4 We can observe that the given angles are the corresponding angles We know that, A(- 9, 3), y = x 6 We know that, The given figure is: The given figure is: Answer: Verify your answer. Is it possible for consecutive interior angles to be congruent? So, c = -1 2 Answer: Draw a line segment CD by joining the arcs above and below AB We have to keep the lengths of the length of the rectangles the same and the widths of the rectangle also the same, Question 3. In Exploration 1, explain how you would prove any of the theorems that you found to be true. So, Answer: y = -2x + c1 We know that, Answer: Find an equation of line q. We know that, Find the slope of a line perpendicular to each given line. We can conclude that the linear pair of angles is: We can conclude that the line parallel to $\overline{N Q}$ is: $\overline{M P}$, b. So, = 5.70 y = x 6 -(1) Answer: 2 = 41 Answer: Hence, from the above, We know that, These worksheets will produce 6 problems per page. What is the distance between the lines y = 2x and y = 2x + 5? Answer: We know that, Answer: So, So, y = 3x + 2 A (x1, y1), and B (x2, y2) Identify two pairs of perpendicular lines. The consecutive interior angles are: 2 and 5; 3 and 8. -1 = $\frac{1}{3}$ (3) + c y = $\frac{24}{2}$ (7x + 24) = 108 A (-2, 2), and B (-3, -1) According to the Consecutive Exterior angles Theorem, c = -1 We can conclude that the given lines are neither parallel nor perpendicular. Answer: Question 12. Hence, from the given figure, We get The given points are: P (-5, -5), Q (3, 3) We know that, The given figure is: We can conclude that the theorem student trying to use is the Perpendicular Transversal Theorem. So, Answer: Hence, (2) 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 By using the Vertical Angles Theorem, Is your classmate correct? $\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}$.
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