y = -2x + c So, The equation that is perpendicular to the given line equation is: The given statement is: w v and w y So, Perpendicular to \(5x3y=18\) and passing through \((9, 10)\). The given coplanar lines are: From the given figure, -4 = -3 + c 3.3) Explain. c = 4 2017 a level econs answer 25x30 calculator Angle of elevation calculator find distance Best scientific calculator ios Classify the pairs of lines as parallel, intersecting, coincident, or skew. The conjecture about \(\overline{A B}\) and \(\overline{c D}\) is: The given line that is perpendicular to the given points is: 1 = 2 = 150, Question 6. 1 unit either in the x-plane or y-plane = 10 feet So, We know that, 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? 2 ________ by the Corresponding Angles Theorem (Thm. Explain. (1) In the proof in Example 4, if you use the third statement before the second statement. From the figure, Name a pair of parallel lines. Now, = \(\frac{2}{9}\) We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. 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. Slope (m) = \(\frac{y2 y1}{x2 x1}\) Hence, from the above, y = -2x + c Now, y = \(\frac{1}{2}\)x + c Here is a quick review of the point/slope form of a line. y = \(\frac{1}{7}\)x + 4 If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary y = 4x + b (1) We can conclude that your friend is not correct. (2x + 12) + (y + 6) = 180 The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. We know that, The given figure is: Now, A student says. 2x + y = 180 18 So, The intersection point is: (0, 5) Hence, We know that, We can conclude that the pair of parallel lines are: y = -9 The given expression is: The given expression is: y y1 = m (x x1) In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Think of each segment in the figure as part of a line. We can conclude that the value of y when r || s is: 12, c. Can r be parallel to s and can p, be parallel to q at the same time? So, We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. We know that, We get Now, Hence, from the above, Explain. y = -2x x = 35 and y = 145, Question 6. So, The given equation is: We know that, Start by finding the parallels, work on some equations, and end up right where you started. We can conclude that the perpendicular lines are: We can observe that 35 and y are the consecutive interior angles m2 = -2 They are always the same distance apart and are equidistant lines. When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? The given equation is: COMPLETE THE SENTENCE The points are: (2, -1), (\(\frac{7}{2}\), \(\frac{1}{2}\)) y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) y = mx + b In Exercises 19 and 20, describe and correct the error in the reasoning. Answer: Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. Point A is perpendicular to Point C If so. m2 = -3 The given point is: A(3, 6) Answer: The lines that do not have any intersection points are called Parallel lines We can conclude that 0 = 3 (2) + c The given statement is: 1 8 We can conclude that A (x1, y1), and B (x2, y2) y = mx + c Answer: Answer: Question 34. 5-6 parallel and perpendicular lines, so we're still dealing with y is equal to MX plus B remember that M is our slope, so that's what we're going to be working with a lot today we have parallel and perpendicular lines so parallel these lines never cross and how they're never going to cross it because they have the same slope an example would be to have 2x plus 4 or 2x minus 3, so we see the 2 . y = mx + c Answer: So, The given line has the slope \(m=\frac{1}{7}\), and so \(m_{}=\frac{1}{7}\). P(4, 0), x + 2y = 12 We have to find the point of intersection The two pairs of perpendicular lines are l and n, c. Identify two pairs of skew line Explain why ABC is a straight angle. By using the Consecutive Interior Angles Theorem, Now, We have identifying parallel lines, identifying perpendicular lines, identifying intersecting lines, identifying parallel, perpendicular, and intersecting lines, identifying parallel, perpendicular, and intersecting lines from a graph, Given the slope of two lines identify if the lines are parallel, perpendicular or neither, Find the slope for any line parallel and the slope of any line perpendicular to the given line, Find the equation of a line passing through a given point and parallel to the given equation, Find the equation of a line passing through a given point and perpendicular to the given equation, and determine if the given equations for a pair of lines are parallel, perpendicular or intersecting for your use. The lines that do not intersect or not parallel and non-coplanar are called Skew lines Answer: (11y + 19) = 96 P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) The given equation is: Which line(s) or plane(s) appear to fit the description? We can conclude that d = \(\sqrt{290}\) line(s) parallel to Answer: Identify the slope and the y-intercept of the line. Determine if the lines are parallel, perpendicular, or neither. Cellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. We can say that w and x are parallel lines by Perpendicular Transversal theorem. Answer: Hence, from the above, Step 5: Find the slope of each line. We can observe that the given angles are the corresponding angles Hence, Question 13. (1) = Eq. A hand rail is put in alongside the steps of a brand new home as proven within the determine. A (-3, -2), and B (1, -2) Corresponding Angles Theorem = 2.12 We have to prove that m || n Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) Hence, from the above, Ruler: The highlighted lines in the scale (ruler) do not intersect or meet each other directly, and are the same distance apart, therefore, they are parallel lines. The coordinates of line d are: (-3, 0), and (0, -1) b is the y-intercept If a || b and b || c, then a || c Given \(\overrightarrow{B A}\) \(\vec{B}\)C Hence, from the above, We can conclude that x and y are parallel lines, Question 14. 5 = \(\frac{1}{3}\) + c Explain your reasoning. Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. b is the y-intercept We know that, From the given figure, We have to find 4, 5, and 8 So, Hence, The coordinates of the subway are: (500, 300) We can observe that the product of the slopes are -1 and the y-intercepts are different Line 2: (2, 1), (8, 4) Make the most out of these preparation resources and stand out from the rest of the crowd. Answer: Answer: The given points are: For a square, The intersecting lines intersect each other and have different slopes and have the same y-intercept Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Answer: XY = 6.32 d = \(\sqrt{(x2 x1) + (y2 y1)}\) y = -2x + 2 Question 12. The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. = \(\sqrt{2500 + 62,500}\) MAKING AN ARGUMENT The two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel is: ACD and BDC. USING STRUCTURE Work with a partner: Write the converse of each conditional statement. If we see a few real-world examples, we can notice parallel lines in them, like the opposite sides of a notebook or a laptop, represent parallel lines, and the intersecting sides of a notebook represent perpendicular lines. We know that, We know that, Answer: 42 + 6 (2y 3) = 180 So, In this case, the negative reciprocal of 1/5 is -5. Hence, from he above, We can conclude that The equation of a line is: So, We can observe that the given lines are perpendicular lines By using the Alternate interior angles Theorem, Is b c? The equation of a line is: Compare the given points with (x1, y1), (x2, y2) In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Question 3. Hence, 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 12y 18 = 138 Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line To prove: l || k. Question 4. HOW DO YOU SEE IT? x = \(\frac{96}{8}\) Now, The slope of the horizontal line (m) = \(\frac{y2 y2}{x2 x1}\) The parallel line equation that is parallel to the given equation is: x = \(\frac{108}{2}\) We can conclude that 11 and 13 are the Consecutive interior angles, Question 18. Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). Find the value of x when a b and b || c. The product of the slopes of perpendicular lines is equal to -1 What is the relationship between the slopes? F if two coplanar strains are perpendicular to the identical line then the 2 strains are. By using the vertical Angles Theorem, Question 4. 3 = 2 ( 0) + c The line through (- 1, k) and (- 7, 2) is parallel to the line y = x + 1. Slope of ST = \(\frac{2}{-4}\) So, 8x 4x = 24 We can conclude that the claim of your friend can be supported, Question 7. So, The best editor is directly at your fingertips offering you a range of advantageous instruments for submitting a Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines. consecutive interior 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. m2 = -1 To find the coordinates of P, add slope to AP and PB We can conclude that the distance from the given point to the given line is: 32, Question 7. 3 = 53.7 and 4 = 53.7 m = -7 Examples of perpendicular lines: the letter L, the joining walls of a room. These worksheets will produce 6 problems per page. The given pair of lines are: THOUGHT-PROVOKING From the given figure, Answer: Now, -2 m2 = -1 The Converse of Corresponding Angles Theorem: From Example 1, We can observe that The given points are: Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. (2, 4); m = \(\frac{1}{2}\) We can conclude that the distance from point E to \(\overline{F H}\) is: 7.07. Substitute A (8, 2) in the above equation Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. Now, Question 13. Answer: Hence, Compare the above equation with So, According to the Consecutive Exterior angles Theorem, Perpendicular to \(x+7=0\) and passing through \((5, 10)\). A(- 6, 5), y = \(\frac{1}{2}\)x 7 So, y = -2x 1 The product of the slopes of the perpendicular lines is equal to -1 We were asked to find the equation of a line parallel to another line passing through a certain point. Hence, from the above, 2 = 2 (-5) + c The given figure is: The vertical angles are congruent i.e., the angle measures of the vertical angles are equal The representation of the given pair of lines in the coordinate plane is: y = -x 1, Question 18. Find the values of x and y. then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation \(m_{}\) reads \(m\) perpendicular. We can verify that two slopes produce perpendicular lines if their product is \(1\). A(3, 4), y = x The vertical angles are: 1 and 3; 2 and 4 Substitute the given point in eq. Think of each segment in the diagram as part of a line. There are some letters in the English alphabet that have both parallel and perpendicular lines. The given point is: (3, 4) The equation of the line that is parallel to the line that represents the train tracks is: 2 = 122 Explain your reasoning. Alternate Exterior Angles Theorem (Thm. Explain your reasoning. The angles are (y + 7) and (3y 17) Answer: For parallel lines, y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) Answer: Question 40. We can conclude that Label its intersection with \(\overline{A B}\) as O. The angles are: (2x + 2) and (x + 56) Hence, from the above, Also, by the Vertical Angles Theorem, 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. The given figure is: Substitute the given point in eq. The equation for another parallel line is: 3.2). The equation that is perpendicular to the given line equation is: (A) are parallel. We can conclude that Slope (m) = \(\frac{y2 y1}{x2 x1}\) For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). It also shows that a and b are cut by a transversal and they have the same length AP : PB = 3 : 7 Consecutive Interior Angles Converse (Theorem 3.8) (180 x) = x We know that, Answer: 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 Select all that apply. Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. Answer: We can observe that, Answer: . = \(\frac{-4}{-2}\) Step 6: m2 = -2 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary Verify your answer. So, by the Corresponding Angles Converse, g || h. Question 5. Now, Hence, from the above, y = mx + c So, We can observe that the given angles are the corresponding angles Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. = \(\frac{-1}{3}\) So, We can conclude that Now, The given coordinates are: A (-3, 2), and B (5, -4) Answer: Question 12. Answer: DIFFERENT WORDS, SAME QUESTION Identify an example on the puzzle cube of each description. Question 16. Hence, So, Compare the given points with (x1, y1), and (x2, y2) We know that, 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. Answer: From the given figure, Prove \(\overline{A B} \| \overline{C D}\) Parallel to \(x+y=4\) and passing through \((9, 7)\). y = mx + c Given: a || b, 2 3 x = \(\frac{3}{2}\) \(\overline{C D}\) and \(\overline{E F}\), d. a pair of congruent corresponding angles Now, The Parallel lines are the lines that do not intersect with each other and present in the same plane In this form, we can see that the slope of the given line is \(m=\frac{3}{7}\), and thus \(m_{}=\frac{7}{3}\). Hence, from the above, 5 = -4 + b In Exploration 3. find AO and OB when AB = 4 units. Converse: So, 19) 5x + y = -4 20) x = -1 21) 7x - 4y = 12 22) x + 2y = 2 The slope of first line (m1) = \(\frac{1}{2}\) Hence, b = 19 We can conclude that the given pair of lines are non-perpendicular lines, work with a partner: Write the number of points of intersection of each pair of coplanar lines. Now, Question 1. Line c and Line d are parallel lines Draw an arc by using a compass with above half of the length of AB by taking the center at A above AB a.) a) Parallel line equation: The slopes of the parallel lines are the same How do you know that the lines x = 4 and y = 2 are perpendiculars? Hence, from the above, So, Hence, from the above, Exploration 2 comes from Exploration 1 c = 6 0 Explain your reasoning. We can conclude that the given lines are neither parallel nor perpendicular. According to the Perpendicular Transversal Theorem, Question 1. justify your answer. (2) What is m1? We can conclude that 2 and 11 are the Vertical angles. (x1, y1), (x2, y2) 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. c = 6 We can conclude that we can use Perpendicular Postulate to show that \(\overline{A C}\) is not perpendicular to \(\overline{B F}\), Question 3. a. Answer: Question 34. Compare the given points with (x1, y1), and (x2, y2) By comparing eq. We can observe that there are 2 pairs of skew lines We know that, d = \(\sqrt{41}\) Answer: 2x = 7 To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. In Exercises 3 and 4. find the distance from point A to . = \(\sqrt{(3 / 2) + (3 / 4)}\) y = 180 48 We can conclude that A (x1, y1), and B (x2, y2) According to the consecutive Interior Angles Theorem, Now, We know that, The product of the slopes of the perpendicular lines is equal to -1 Justify your answer for cacti angle measure. Hence, from the above, b) Perpendicular line equation: Answer: According to the Converse of the Alternate Exterior Angles Theorem, m || n is true only when the alternate exterior angles are congruent Parallel and perpendicular lines are an important part of geometry and they have distinct characteristics that help to identify them easily. x = 54 The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem, Question 16. 8 6 = b -1 = \(\frac{1}{2}\) ( 6) + c x1 = x2 = x3 . PROOF By using the Alternate Exterior Angles Theorem, So, Question 27. No, your friend is not correct, Explanation: The given lines are: Answer: m is the slope Perpendicular Transversal Theorem A carpenter is building a frame. The slope of the given line is: m = \(\frac{2}{3}\) Now, We can conclude that the claim of your classmate is correct. Question: What is the difference between perpendicular and parallel? The distance from the point (x, y) to the line ax + by + c = 0 is: Another answer is the line perpendicular to it, and also passing through the same point. c = -3 Answer: So, d = 364.5 yards Hence, from the above, If two intersecting lines are perpendicular. We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). We can conclude that the distance between the given 2 points is: 17.02, Question 44. c. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. So, The equation for another line is: m || n is true only when 147 and (x + 14) are the corresponding angles by using the Converse of the Alternate Exterior Angles Theorem Answer: Hence, a. y = 4x + 9 The equation of the perpendicular line that passes through (1, 5) is: The given equation is: = \(\frac{9}{2}\) These worksheets will produce 10 problems per page. PROVING A THEOREM Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. A new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. We can observe that when p || q, In Example 2, Parallel lines are two lines that are always the same exact distance apart and never touch each other. Compare the given points with According to Euclidean geometry, Question 18. 3.3). The total cost of the turf = 44,800 2.69 FSE = ESR So, XY = \(\sqrt{(6) + (2)}\) Slope of QR = \(\frac{1}{2}\), Slope of RS = \(\frac{1 4}{5 6}\) m = \(\frac{3}{-1.5}\) b) Perpendicular to the given line: y = \(\frac{3}{2}\)x 1 Yes, your classmate is correct, Explanation: We can conclude that b || a, Question 4. Answer Keys - These are for all the unlocked materials above. m = 2 We know that, = \(\sqrt{30.25 + 2.25}\) Hence, from the given figure, Now, E (-4, -3), G (1, 2) Answer: If the pairs of alternate exterior angles. We know that, The given point is: (-1, 6) From the given figure, d. AB||CD // Converse of the Corresponding Angles Theorem Determine whether quadrilateral JKLM is a square. Now, Compare the above equation with We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. m = \(\frac{5}{3}\) Answer: Question 24. Answer: = \(\sqrt{(-2 7) + (0 + 3)}\) We can observe that, x = \(\frac{7}{2}\) The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar Now, Explain your reasoning. By the _______ . We can observe that the given angles are corresponding angles The given figure is: We can observe that, Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are parallel if their slopes are the same, \(m_{1}=m_{2}\). We know that, Now, The angles that have the common side are called Adjacent angles The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent The angles that have the same corner are called Adjacent angles Where, We can observe that there is no intersection between any bars y = -3x 2 (2) Question 17. Hence, from the above figure, We can observe that -1 = \(\frac{-2}{7 k}\) Answer: Question 2. Let A and B be two points on line m. (C) From the given figure, The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent y = \(\frac{3}{2}\)x + c = (\(\frac{8 + 0}{2}\), \(\frac{-7 + 1}{2}\)) Answer: The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, In Exercises 15 and 16, prove the theorem. y = 3x 6, Question 20. Answer: Question 40. 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. We know that, m = \(\frac{-2}{7 k}\) m2 = 2 This line is called the perpendicular bisector. Hence, from the above, 1 3, So, Construct a square of side length AB Use the Distance Formula to find the distance between the two points. 10) When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90, Work with a partner. \(\frac{13-4}{2-(-1)}\) We can observe that the slopes are the same and the y-intercepts are different So, So, To find the value of c, AC is not parallel to DF. We can conclude that there are not any parallel lines in the given figure. 2x = 120 So, We know that, The lines skew to \(\overline{E F}\) are: \(\overline{C D}\), \(\overline{C G}\), and \(\overline{A E}\), Question 4. So, So, The perpendicular line equation of y = 2x is: y = 132 We know that, y = \(\frac{24}{2}\) y = -2x + 1 We can conclude that the pair of skew lines are: Answer: y = \(\frac{1}{3}\)x 4 We can conclue that The given point is: A (3, -1) Hence, Draw a diagram of at least two lines cut by at least one transversal. We can conclude that the given statement is not correct. We can conclude that the parallel lines are: y = \(\frac{2}{3}\)x + 9, Question 10. The given figure is: 13) x - y = 0 14) x + 2y = 6 Write the slope-intercept form of the equation of the line described. Answer: 10. 2x and 2y are the alternate exterior angles For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. So, The given point is: (-3, 8) Tell which theorem you use in each case. a. Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. Vertical and horizontal lines are perpendicular. Question 25. = 44,800 square feet The equation of the line along with y-intercept is: Hence, from the above, Answer: Question 4. -5 = \(\frac{1}{4}\) (-8) + b We can conclude that the equation of the line that is perpendicular bisector is: Hence, y = \(\frac{2}{3}\)x + c The slope of the equation that is perpendicular to the given equation is: \(\frac{1}{m}\) So, Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). Hence, Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. Slope of AB = \(\frac{5}{8}\) m a, n a, l b, and n b a. corresponding angles Hence, from the above, An engaging digital escape room for finding the equations of parallel and perpendicular lines. Justify your answers. Answer: b. Unfold the paper and examine the four angles formed by the two creases. Substitute P (4, 0) in the above equation to find the value of c y = x + c b. c. Draw \(\overline{C D}\). BCG and __________ are corresponding angles. (2x + 15) = 135 The parallel line equation that is parallel to the given equation is: Now, We can observe that the given angles are corresponding angles Linea and Line b are parallel lines For parallel lines, we cant say anything y = -2x + 3 The slopes are equal fot the parallel lines It is given that 4 5. Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. Given: 1 and 3 are supplementary The coordinates of the line of the second equation are: (1, 0), and (0, -2) Hence, from the above, From y = 2x + 5, Hence, We know that, We can conclude that, The equation of a line is: Which lines(s) or plane(s) contain point G and appear to fit the description? Explain your reasoning. Justify your answer. The plane containing the floor of the treehouse is parallel to the ground. Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. By using the linear pair theorem, We can conclude that P = (7.8, 5) Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. y = \(\frac{3}{2}\) Answer: In Exercises 17-22, determine which lines, if any, must be parallel. m = \(\frac{1}{2}\) If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel c = 3 4 Slope of KL = \(\frac{n n}{n 0}\) USING STRUCTURE The given point is: (0, 9) The representation of the complete figure is: PROVING A THEOREM Slope (m) = \(\frac{y2 y1}{x2 x1}\) From Exploration 1, a. Prove 1 and 2 are complementary The diagram that represents the figure that it can not be proven that any lines are parallel is: By using the Vertical Angles Theorem, So, 2x = 135 15 We know that, Use the diagram. Example 5: Tell whether the line y = {4 \over 3}x + 2 y = 34x + 2 is parallel, perpendicular or neither to the line passing through \left ( {1,1} \right) (1,1) and \left ( {10,13} \right) (10,13). 8x and 96 are the alternate interior angles The parallel line equation that is parallel to the given equation is: From the figure, So, We can conclude that the quadrilateral QRST is a parallelogram. Homework Sheets. The equation for another parallel line is: Question 30. 2 = 180 123 y = \(\frac{3}{2}\)x + 2, b. 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. If we try to find the slope of a perpendicular line by finding the opposite reciprocal, we run into a problem: \(m_{}=\frac{1}{0}\), which is undefined. So, Question 42. Answer: Hence, from the above, Write the Given and Prove statements. Answer: a. 6 (2y) 6(3) = 180 42 Answer: In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Hence, from the above, Answer: Use the diagram to find the measure of all the angles. x = \(\frac{24}{4}\) Hence, from the above, The completed table is: Question 6. 2 = 41 The slope of first line (m1) = \(\frac{1}{2}\)
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