The equation of the line that is perpendicular to the given line equation is: They are not parallel because they are intersecting each other. Answer: Horizontal and vertical lines are perpendicular to each other. From the given figure, c = -4 The given point is: A (-6, 5) y = -x + c Question 5. Answer: We can observe that the given pairs of angles are consecutive interior angles The given figure is: A(1, 6), B(- 2, 3); 5 to 1 Answer: We can conclude that Now, c = -2 The given coplanar lines are: 5 7 The slope of the equation that is parallel t the given equation is: 3 The given points are: P (-5, -5), Q (3, 3) c = -1 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. Explain. y = \(\frac{1}{2}\)x + c 3 = 180 133 k = -2 + 7 m is the slope The equation of the line that is perpendicular to the given line equation is: 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 y y1 = m (x x1) The representation of the given pair of lines in the coordinate plane is: We know that, From the figure, The equation for another line is: We have to divide AB into 5 parts From the given figure, 0 = \(\frac{1}{2}\) (4) + c Answer: Question 20. The point of intersection = (\(\frac{7}{2}\), \(\frac{1}{2}\)) Hence, The given points are: Hence, from the above, Answer: Question 8. Solution: Using the properties of parallel and perpendicular lines, we can answer the given . PROOF So, y = \(\frac{8}{5}\) 1 Answer: 1 = 2 = 133 and 3 = 47. (A) are parallel. The equation of the line that is parallel to the given equation is: From Exploration 1, The equation of the line along with y-intercept is: Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. \(\frac{1}{2}\) (m2) = -1 Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Hence, from the above, Perpendicular lines have slopes that are opposite reciprocals. Answer: Question 10. Compare the given equation with Substitute A (3, -1) in the above equation to find the value of c The corresponding angles are: and 5; 4 and 8, b. alternate interior angles From the given figure, 5 = 4 (-1) + b \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). Section 6.3 Equations in Parallel/Perpendicular Form. From the given figure, a. 1 = 180 57 y = \(\frac{1}{2}\)x 2 m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem a.) The sides of the angled support are parallel. 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. c = -2 Answer: Question 12. So, y = \(\frac{1}{3}\)x + c 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. Hence, from the above, The given point is: (6, 4) Question 22. The missing information the student assuming from the diagram is: Answer: The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 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. Draw \(\overline{C D}\). We can conclude that (B) intersect Exploration 2 comes from Exploration 1 = (4, -3) According to the consecutive exterior angles theorem, XY = \(\sqrt{(3 + 1.5) + (3 2)}\) It is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. So, From the given figure, So, If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary The diagram that represents the figure that it can be proven that the lines are parallel is: Question 33. Once the equation is already in the slope intercept form, you can immediately identify the slope. y = -2x + 2. By using the Perpendicular transversal theorem, Now, By using the Alternate interior angles Theorem, Question 4. A(8, 0), B(3, 2); 1 to 4 REASONING A(0, 3), y = \(\frac{1}{2}\)x 6 We know that, (\(\frac{1}{3}\)) (m2) = -1 an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). Determine whether quadrilateral JKLM is a square. You and your family are visiting some attractions while on vacation. Answer: We know that, When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. = \(\frac{0}{4}\) (b) perpendicular to the given line. 2 = 57 x and 97 are the corresponding angles Question 20. Prove 2 4 We can conclude that We can observe that 141 and 39 are the consecutive interior angles Converse: y = mx + c We can observe that Hence, from the above, 1 + 2 = 180 b) Perpendicular to the given line: From the figure, y = mx + c 2 = 133 y = -2x + 1, e. Draw the portion of the diagram that you used to answer Exercise 26 on page 130. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. To do this, solve for \(y\) to change standard form to slope-intercept form, \(y=mx+b\). We can conclude that the value of x is: 54, Question 3. m = \(\frac{-30}{15}\) y = \(\frac{1}{2}\)x + c Linea and Line b are parallel lines Lines Perpendicular to a Transversal Theorem (Thm. Hence, from the above, Answer: Question 25. 2x = 120 The given figure is: then they are congruent. Find the slope of a line perpendicular to each given line. Slope of MJ = \(\frac{0 0}{n 0}\) What shape is formed by the intersections of the four lines? Compare the above equation with We can observe that Substitute (2, -2) in the above equation The given figure is: : n; same-side int. 1 = 2 We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. From the given figure, We can conclude that the value of XY is: 6.32, Find the distance from line l to point X. The equation for another line is: XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) Prove: AB || CD Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent We know that, 1 + 138 = 180 = \(\frac{8}{8}\) (1) = \(\frac{-1 3}{0 2}\) Label the intersections as points X and Y. Answer: m1m2 = -1 Compare the given equation with b.) c = -6 The Coincident lines may be intersecting or parallel = \(\frac{3 2}{-2 2}\) (2) to get the values of x and y Hence, from the above, The length of the field = | 20 340 | x = 23 Identify all pairs of angles of the given type. The given equation is: y = \(\frac{1}{5}\)x + c 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 XZ = 7.07 So, (-3, 7), and (8, -6) = 2 Simply click on the below available and learn the respective topics in no time. Substitute (2, -3) in the above equation PROBLEM-SOLVING We know that, We can conclude that the claim of your friend can be supported, Question 7. We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) The given equation is: According to the Converse of the Interior Angles Theory, m || n is true only when the sum of the interior angles are supplementary = 0 We get So, If you use the diagram below to prove the Alternate Exterior Angles Converse. From the given figure, CONSTRUCTION Now, The given figure is: So, (2) Name a pair of perpendicular lines. d = \(\sqrt{(x2 x1) + (y2 y1)}\) The representation of the given coordinate plane along with parallel lines is: c = -9 3 It is given that m || n x = y = 61, Question 2. Answer: Question 34. Hence, from the above, 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. So, 8 = 65. These worksheets will produce 6 problems per page. The given pair of lines are: In Exploration 2. find more pairs of lines that are different from those given. R and s, parallel 4. consecutive interior Question 1. 2x = 180 72 The lines that have an angle of 90 with each other are called Perpendicular lines Algebra 1 Parallel and Perpendicular lines What is the equation of the line written in slope-intercept form that passes through the point (-2, 3) and is parallel to the line y = 3x + 5? Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. 2 = 180 3 -1 = \(\frac{1}{2}\) ( 6) + c 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. = 6.26 MATHEMATICAL CONNECTIONS y = \(\frac{2}{3}\)x + b (1) 2x = 135 15 P(0, 1), y = 2x + 3 Answer: 8 = 105, Question 2. The given figure is: Substitute the given point in eq.
Parallel and Perpendicular Lines Digital Math Escape Room The representation of the given point in the coordinate plane is: Question 56. Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. The given coordinates are: A (1, 3), and B (8, 4) The given figure is: Now, 4. 2y and 58 are the alternate interior angles Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither Perpendicular Transversal Theorem A carpenter is building a frame. The given equation is: These guidelines, with the editor will assist you with the whole process. The equation that is parallel to the given equation is: 1 and 8 are vertical angles It is given that m || n that passes through the point (2, 1) and is perpendicular to the given line. It is given that Write a conjecture about the resulting diagram. c = 3 The rungs are not intersecting at any point i.e., they have different points We can conclude that the linear pair of angles is: Now, We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) y 175 = \(\frac{1}{3}\) (x -50) In Example 5. yellow light leaves a drop at an angle of m2 = 41. y = \(\frac{1}{3}\)x + c WRITING We can observe that Work with a partner: Fold a piece of pair in half twice. We know that, The given figure is: Explain your reasoning. -x x = -3 = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) 140 21 32 = 6x We have to find the point of intersection So, 8x = 118 6 When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. Mark your diagram so that it cannot be proven that any lines are parallel. Hence, so they cannot be on the same plane. The slope of second line (m2) = 1 \(\frac{6 (-4)}{8 3}\) Question: What is the difference between perpendicular and parallel? So, (2x + 20)= 3x Now, Question 1. The slope of the given line is: m = 4 So, Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. AP : PB = 2 : 6
(4.3.1) - Parallel and Perpendicular Lines - Lumen Learning m2 = \(\frac{1}{2}\), b2 = -1 In Exercises 19 and 20, describe and correct the error in the reasoning. Since k || l,by the Corresponding Angles Postulate, 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. The given point is: A (8, 2) To find the distance from point A to \(\overline{X Z}\), Given m1 = 115, m2 = 65 y = \(\frac{1}{3}\)x + c The perpendicular equation of y = 2x is: Now, Which lines intersect ? b) Perpendicular line equation: 2x = -6 y = 12 (2) 3 = -2 (-2) + c We can observe that when r || s, The slope of the horizontal line (m) = \(\frac{y2 y2}{x2 x1}\) We can conclude that Now, Perpendicular lines always intersect at 90. 2 = 123 Use the photo to decide whether the statement is true or false. Now, x = 12 To find the value of c, substitute (1, 5) in the above equation To find the value of b, m = \(\frac{-2}{7 k}\) 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. In Exploration 1, explain how you would prove any of the theorems that you found to be true. It is given that 4 5. Parallel lines We know that, Slope (m) = \(\frac{y2 y1}{x2 x1}\) d. AB||CD // Converse of the Corresponding Angles Theorem Hence, from the above, Justify your conjecture. We can conclude that XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We can conclue that THOUGHT-PROVOKING x = 4 as corresponding angles formed by a transversal of parallel lines, and so, The given point is: A (-\(\frac{1}{4}\), 5) Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). Answer: Question 6. The representation of the given pair of lines in the coordinate plane is: Prove 1 and 2 are complementary We can conclude that m || n by using the Consecutive Interior angles Theorem, Question 13. = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) We can observe that the product of the slopes are -1 and the y-intercepts are different ax + by + c = 0 a. Hence, The product of the slopes of perpendicular lines is equal to -1 The given point is: (-8, -5) We know that, Answer: -3 = 9 + c The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem, Question 16. If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept The given point is: A (3, -4) We can observe that Now, 3x 5y = 6 Parallel to \(y=3\) and passing through \((2, 4)\). The given pair of lines are: perpendicular lines. x = 90 We will use Converse of Consecutive Exterior angles Theorem to prove m || n y = 3x 6, Question 20. y = mx + c We can conclude that the value of x is: 60, Question 6. So, Which is different? Slope of TQ = 3 From the above diagram, Slope (m) = \(\frac{y2 y1}{x2 x1}\) So, So, Answer: 9 and x- Answer: 2 and y Answer: x +15 and Answer: x +10 2 x -6 and 2x + 3y Answer: 6) y and 3x+y=- Answer: Answer: 14 and y = 5 6 P(3, 8), y = \(\frac{1}{5}\)(x + 4) We can conclude that m1 m2 = -1 y = \(\frac{13}{5}\) 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 We can conclude that Use a graphing calculator to verify your answer. 9. We know that, m1m2 = -1 If the pairs of alternate interior angles are, Answer: 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. Step 2: Hence, from the above, In Exercises 11-14, identify all pairs of angles of the given type. Answer: y = -3 The equation that is perpendicular to the given line equation is: = 1.67 Using the same compass selling, draw an arc with center B on each side \(\overline{A B}\). According to the Perpendicular Transversal Theorem, Homework Sheets. c = -1 1 If line E is parallel to line F and line F is parallel to line G, then line E is parallel to line G. Question 49. From the given figure, Hence, 19) 5x + y = -4 20) x = -1 21) 7x - 4y = 12 22) x + 2y = 2 The conjectures about perpendicular lines are: Write a conjecture about \(\overline{A O}\) and \(\overline{O B}\) Justify your conjecture. We can observe that the product of the slopes are -1 and the y-intercepts are different = 1
PDF Parallel and Perpendicular Lines : Shapes Sheet 1 - Math Worksheets 4 Kids = | 4 + \(\frac{1}{2}\) | 2 = 122, Question 16. The equation that is perpendicular to the given equation is: We know that, c = 1 If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. EG = \(\sqrt{(5) + (5)}\) The slope that is perpendicular to the given line is: From the given figure, Explain your reasoning. To use the "Parallel and Perpendicular Lines Worksheet (with Answer Key)" use the clues in identifying whether two lines are parallel or perpendicular with each other using the slope. So, The lines skew to \(\overline{E F}\) are: \(\overline{C D}\), \(\overline{C G}\), and \(\overline{A E}\), Question 4. Name the line(s) through point F that appear skew to . So, The equation of the perpendicular line that passes through (1, 5) is: So, PROVING A THEOREM y = -x + c Therefore, they are parallel lines. Answer: Question 14. From the given figure, Justify your answer with a diagram. So, So, by the _______ , g || h. Answer: the equation that is perpendicular to the given line equation is: Now, Compare the given points with 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. Which of the following is true when are skew? Hence, y = \(\frac{2}{3}\)x + 9, Question 10. = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) According to Corresponding Angles Theorem, Now, line(s) parallel to The standard form of the equation is: Vertical and horizontal lines are perpendicular. Hence, from the above, Answer: Question 2. Answer: The representation of the given pair of lines in the coordinate plane is: c = -12 2x + 4y = 4 m = 2 8x = (4x + 24) Compare the given coordinates with (x1, y1), and (x2, y2) 2x = 108 Answer: Explain your reasoning. So, Step 4: We know that, We can observe that k 7 = -2 So, XY = 6.32 a. = \(\frac{50 500}{200 50}\) Answer: Question 4. Is it possible for consecutive interior angles to be congruent? Hence, Now, We can conclude that the value of x is: 12, Question 10. Find the distance front point A to the given line. According to the Corresponding Angles Theorem, the corresponding angles are congruent So, Hence,
Unit 3 Test Parallel And Perpendicular Lines Answer Key Pdf - Fill According to the Vertical Angles Theorem, the vertical angles are congruent The given figure is: a. c.) Parallel lines intersect each other at 90. c is the y-intercept We know that, The values of AO and OB are: 2 units, Question 1. x = \(\frac{96}{8}\) Hence, Select the orange Get Form button to start editing. Where, line(s) perpendicular to (1) and eq.
Quiz: Parallel and Perpendicular Lines - Quizizz The line through (- 1, k) and (- 7, 2) is parallel to the line y = x + 1. BCG and __________ are corresponding angles. These worksheets will produce 10 problems per page. According to the Vertical Angles Theorem, the vertical angles are congruent You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. y = \(\frac{1}{7}\)x + 4 d = | x y + 4 | / \(\sqrt{1 + (-1)}\) So, We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14.
PDF Infinite Geometry - Parallel and Perpendicular slopes HW - Disney II Magnet 8 = -2 (-3) + b Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line It is given that m || n One way to build stairs is to attach triangular blocks to angled support, as shown. We have to divide AB into 8 parts Let A and B be two points on line m. Answer: Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. NAME _____ DATE _____ PERIOD _____ Chapter 4 26 Glencoe Algebra 1 4-4 Skills Practice Parallel and Perpendicular Lines No, there is no enough information to prove m || n, Question 18. Slope of LM = \(\frac{0 n}{n n}\) Perpendicular lines are intersecting lines that always meet at an angle of 90. Find the equation of the line passing through \((1, 5)\) and perpendicular to \(y=\frac{1}{4}x+2\). The line l is also perpendicular to the line j We know that, Perpendicular to \(5x3y=18\) and passing through \((9, 10)\). Answer: What is the perimeter of the field? 5 = -4 + b Now, So, 3.12) The coordinates of a quadrilateral are: Hence, from the above, The given lines are the parallel lines Verticle angle theorem: The coordinates of the midpoint of the line segment joining the two houses = (150, 250) Use the diagram Question 25. Line c and Line d are perpendicular lines, Question 4. We can say that any parallel line do not intersect at any point We can conclude that 44 and 136 are the adjacent angles, b. From the argument in Exercise 24 on page 153, We know that, The given equation is: We can observe that the given angles are the consecutive exterior angles We can conclude that We can conclude that The equation for another line is: y = 2x + c2, b. Now, Hence,f rom the above, The given line equation is: By using the dynamic geometry, The given equation is: (1) = Eq. The general steps for finding the equation of a line are outlined in the following example. So, The Parallel lines have the same slope but have different y-intercepts In spherical geometry. as shown. The lines that do not intersect and are not parallel and are not coplanar are Skew lines y = \(\frac{1}{2}\)x + 2 So, 2: identify a parallel or perpendicular equation to a given graph or equation. \(\frac{1}{2}\) . Hence, from the above, If the pairs of alternate exterior angles. 1 = 53.7 and 5 = 53.7 y = -2x Answer: Question 40. Question 21. Answer: c = \(\frac{40}{3}\) It is given that In Exercises 13 and 14, prove the theorem. (1) The representation of the given point in the coordinate plane is: Question 54. Find the slope \(m\) by solving for \(y\). So, y = \(\frac{10 12}{3}\) A(15, 21), 5x + 2y = 4 So,
Equations parallel and perpendicular lines answer key Now, We know that, Now, Hence, So, When we compare the converses we obtained from the given statement and the actual converse, The given equation is: Respond to your classmates argument by justifying your original answer. So, We can conclude that the tallest bar is parallel to the shortest bar, b. m || n is true only when 147 and (x + 14) are the corresponding angles by using the Converse of the Alternate Exterior Angles Theorem Now, According to Contradiction, a.) c. m5=m1 // (1), (2), transitive property of equality Now, Now, -4 = -3 + c So, y = mx + c By comparing the given pair of lines with The construction of the walls in your home were created with some parallels. y = \(\frac{1}{3}\) (10) 4 Find the distance from the point (6, 4) to the line y = x + 4. We know that, The parallel line needs to have the same slope of 2. By using the Corresponding angles Theorem, c = -2 y = 3x 5 By using the vertical Angles Theorem, Now, The given figure is: Answer: The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. The given line has slope \(m=\frac{1}{4}\), and thus \(m_{}=+\frac{4}{1}=4\). Hence, from the above, Answer: 42 + 6 (2y 3) = 180 A group of campers ties up their food between two parallel trees, as shown. Hence those two lines are called as parallel lines. y = mx + b The given point is: A (3, -1) We know that, What is the distance that the two of you walk together? The product of the slopes of the perpendicular lines is equal to -1 Question 3. c = -2 m = 3 We can solve it by using the "point-slope" equation of a line: y y1 = 2 (x x1) And then put in the point (5,4): y 4 = 2 (x 5) That is an answer! Answer: Question 24. Answer: The slopes of the parallel lines are the same Homework 1 - State whether the given pair of lines are parallel. We know that, The given figure is: We know that, From the above table, y = \(\frac{1}{2}\)x + 6 We know that, We know that, The given point is: (-1, -9) Answer: Is your friend correct? Answer: = 3 y = \(\frac{1}{3}\)x 2 -(1) Answer: = \(\frac{-1 0}{0 + 3}\) We can conclude that how many right angles are formed by two perpendicular lines? We know that, Answer: Question 24. Step 5: Answer: Question 36. From the given figure, From the given figure, a. m1 + m8 = 180 //From the given statement The given point is: A (3, 4) m is the slope A gazebo is being built near a nature trail. y = 132 Perpendicular lines are denoted by the symbol . 3 + 133 = 180 (By using the Consecutive Interior angles theorem) Does the school have enough money to purchase new turf for the entire field? Consecutive Interior Angles Converse (Theorem 3.8) Hence, from the above, Equations of vertical lines look like \(x=k\). So, Indulging in rote learning, you are likely to forget concepts. 1 = 76, 2 = 104, 3 = 76, and 4 = 104, Work with a partner: Use dynamic geometry software to draw two parallel lines. From the given figure, The coordinates of the quadrilateral QRST is: y = mx + b 8x = 112 The standard linear equation is: So, If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. b. We can conclude that the perpendicular lines are: = \(\frac{8}{8}\) 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 8x = 42 2 We know that, Hence, from the above, The points of intersection of intersecting lines: Question 13. No, the third line does not necessarily be a transversal, Explanation: (- 1, 5); m = 4 So, 3. a is perpendicular to d and b is perpendicular to c Write an equation of the line passing through the given point that is perpendicular to the given line. d = \(\sqrt{290}\) \(\frac{1}{3}\)x 2 = -3x 2 Hence, from the above, m is the slope We get m1m2 = -1 -x x = -3 4 We can observe that y = 0.66 feet Compare the given equation with Let the congruent angle be P m = \(\frac{3}{1.5}\) Answer: This can be expressed mathematically as m1 m2 = -1, where m1 and m2 are the slopes of two lines that are perpendicular. Answer: ax + by + c = 0 Hence, from the above, It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor Substitute A (-3, 7) in the above equation to find the value of c c = \(\frac{8}{3}\) Explain your reasoning. Proof of Alternate exterior angles Theorem: We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. By using the Consecutive Interior Angles Theorem, are parallel, or are the same line. Find an equation of line q. The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). b. \(\frac{1}{2}\) (m2) = -1 11y = 96 19 = 0 then the pairs of consecutive interior angles are supplementary. y = \(\frac{1}{2}\)x + b (1)