parallel and perpendicular lines answer key

We can conclude that the value of k is: 5. The Converse of the Consecutive Interior angles Theorem: y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 Hence, from the given figure, The given figure shows that angles 1 and 2 are Consecutive Interior angles y = mx + c Answer: d = \(\sqrt{(x2 x1) + (y2 y1)}\) y = -2x The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. If two lines are intersected by a third line, is the third line necessarily a transversal? The equation of the line that is parallel to the given equation is: By using the Vertical Angles Theorem, We know that, Answer: Question 40. The equation that is perpendicular to the given equation is: Answer: y = \(\frac{3}{2}\)x 1 = 2, The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) We know that, The lines that have an angle of 90 with each other are called Perpendicular lines Answer: The Converse of the consecutive Interior angles Theorem states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. Now, Hence, Answer: y = \(\frac{1}{5}\)x + \(\frac{4}{5}\) From the given figure, The coordinates of x are the same. c. Draw \(\overline{C D}\). We can observe that 1 and 2 are the consecutive interior angles y = mx + b Parallel to \(x+4y=8\) and passing through \((1, 2)\). = \(\frac{3 2}{-2 2}\) Now, So, Hence, from the above figure, So, 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 \(1\). Hence, x + 2y = 2 The given figure is: 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. The given figure is: P = (4, 4.5) So, So, The angles are: (2x + 2) and (x + 56) We know that, Answer: Question 26. Now, Likewise, parallel lines become perpendicular when one line is rotated 90. If the slopes of two distinct nonvertical lines are equal, the lines are parallel. Now, b is the y-intercept How are they different? x = 5 We know that, It is given that The converse of the given statement is: We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. We will use Converse of Consecutive Exterior angles Theorem to prove m || n The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. The equation that is perpendicular to y = -3 is: It is given that 1 = 105 Hence, from the above figure, CRITICAL THINKING line(s) skew to . Now, So, Perpendicular to \(x+7=0\) and passing through \((5, 10)\). To find the coordinates of P, add slope to AP and PB then they are parallel to each other. 48 + y = 180 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. They are always the same distance apart and are equidistant lines. Answer: ERROR ANALYSIS These worksheets will produce 6 problems per page. A group of campers ties up their food between two parallel trees, as shown. These worksheets will produce 6 problems per page. Given: a || b, 2 3 The given equation is: The coordinates of line q are: Substitute A (3, -4) in the above equation to find the value of c Now, y = -2x + \(\frac{9}{2}\) (2) XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) According to the Perpendicular Transversal Theorem, The representation of the given pair of lines in the coordinate plane is: m is the slope y = x 6 -(1) consecutive interior -x x = -3 a n, b n, and c m To find the value of c, substitute (1, 5) in the above equation The given figure is: Now, Answer: We can say that y = \(\frac{5}{3}\)x + c We can conclude that A (-2, 2), and B (-3, -1) So, y = 3x 6, Question 20. Question 22. Answer: Hence, from the above, Answer: Question 29. Draw an arc with center A on each side of AB. We know that, The line that is perpendicular to the given equation is: y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) = \(\frac{-2}{9}\) We can conclude that a || b. Answer: Question 2. Hence, from the above, From the given figure, 3.12) Hence, from the above, Substitute (2, -3) in the above equation Any fraction that contains 0 in the denominator has its value undefined Answer: Compare the given equations with The letter A has a set of perpendicular lines. Parallel to \(x=2\) and passing through (7, 3)\). \(\frac{3}{2}\) . The slope of the parallel line that passes through (1, 5) is: 3 Answer: Now, We know that, The given lines are the parallel lines x = 29.8 (\(\frac{1}{3}\)) (m2) = -1 We get, Compare the given points with They both consist of straight lines. We know that, Answer: 72 + (7x + 24) = 180 (By using the Consecutive interior angles theory) m = -2 4.5 Equations of Parallel and Perpendicular Lines Solving word questions So, Hence, The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) y = 7 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, Enter your answer in the box y=2/5x2 P = (7.8, 5) (- 3, 7) and (8, 6) By using the parallel lines property, Answer: According to the Corresponding Angles Theorem, the corresponding angles are congruent (2) m = \(\frac{1}{4}\) Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line. So, These worksheets will produce 10 problems per page. y = \(\frac{2}{3}\) x = \(\frac{87}{6}\) The given coplanar lines are: Line 2: (2, 1), (8, 4) The equation of a line is: Hence, from the above, Answer: Find the other angle measures. 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. Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. 5 = 105, To find 8: a. a. Hence, from the above, 2x + y = 180 18 Hence, from the coordinate plane, = 1 Hence, from the above, perpendicular, or neither. y = \(\frac{1}{3}\)x + \(\frac{16}{3}\), Question 5. We can say that any coincident line do not intersect at any point or intersect at 1 point Answer: From the above, Geometry chapter 3 parallel and perpendicular lines answer key Apps can be a great way to help learners with their math. Explain. m = -7 The given point is: (-5, 2) Explain your reasoning. Hence, from the above, P || L1 If two intersecting lines are perpendicular. Answer: By comparing the given pair of lines with To find the coordinates of P, add slope to AP and PB = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) Explain your reasoning. Answer: We can observe that the given angles are the consecutive exterior angles 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 We know that, m2 = 1 Hence, Answer: 2 and7 We can conclude that Answer: d = | ax + by + c| /\(\sqrt{a + b}\) So, So, Now, = (-1, -1) d = 17.02 We know that, y = 3x 5 10) So, Can you find the distance from a line to a plane? c = -2 c = 3 y = 4x 7 Question 4. Question 1. So, as shown. Write an equation of the line that passes through the point (1, 5) and is The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. -4 = \(\frac{1}{2}\) (2) + b Answer: Hence, from the above, Now, So, Question 25. We can conclude that we can not find the distance between any two parallel lines if a point and a line is given to find the distance, Question 2. \(\frac{5}{2}\)x = 2 Answer: Question 2. a. From the given figure, The equation of the line that is parallel to the given line equation is: Which rays are not parallel? x = \(\frac{180}{2}\) XY = 6.32 Select all that apply. THINK AND DISCUSS, PAGE 148 1. The given points are: Here 'a' represents the slope of the line. We can conclude that Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. Geometrically, we see that the line \(y=4x1\), shown dashed below, passes through \((1, 5)\) and is perpendicular to the given line. The Intersecting lines have a common point to intersect So, -3 = -2 (2) + c We can conclude that the line parallel to \(\overline{N Q}\) is: \(\overline{M P}\), b. y = \(\frac{3}{2}\) 2 = \(\frac{1}{2}\) (-5) + c 1 = 2 = 123, Question 11. Let A and B be two points on line m. y = x + 9 HOW DO YOU SEE IT? Answer: Question 28. 2m2 = -1 We know that, Solve eq. So, What is m1? Parallel to \(5x2y=4\) and passing through \((\frac{1}{5}, \frac{1}{4})\). We can observe that, Hence, from the above, (Two lines are skew lines when they do not intersect and are not coplanar.) Possible answer: plane FJH 26. plane BCD 2a. In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use. c = 2 We have to find the point of intersection We know that, We know that, So, y = \(\frac{1}{2}\)x + 5 y = \(\frac{3}{5}\)x \(\frac{6}{5}\) Eq. d = \(\frac{4}{5}\) Converse: The given equation is: a. Now, Answer: c = 2 1 Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. x = 14.5 and y = 27.4, Question 9. Hence, from the above, Now, The Coincident lines may be intersecting or parallel d = \(\sqrt{41}\) Verify your answer. Answer: We can conclude that 11 and 13 are the Consecutive interior angles, Question 18. We know that, From the given figure, c = -6 If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor x z and y z Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. If we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0 2 = 0 + c We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. Hence, By the Vertical Angles Congruence Theorem (Theorem 2.6). Perpendicular to \(y=x\) and passing through \((7, 13)\). We can conclude that The slopes of perpendicular lines are undefined and 0 respectively = \(\frac{-4}{-2}\) It is given that So, Converse: Corresponding Angles Theorem We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction Answer: For perpediclar lines, By comparing the given pair of lines with We can observe that Given: m5 + m4 = 180 b = -5 (-3, 8); m = 2 c = \(\frac{9}{2}\) We can conclude that b is the y-intercept DRAWING CONCLUSIONS c. m5=m1 // (1), (2), transitive property of equality The equation that is perpendicular to the given equation is: The angles that have the common side are called Adjacent angles Answer: 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. Answer: We know that, In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. y = \(\frac{1}{2}\)x 7 So, y = -x + c According to Corresponding Angles Theorem, Hence, Lines that are parallel to each other will never intersect. The equation of a line is x + 2y = 10. We can conclude that -1 = 2 + c We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. We know that, Answer: Each bar is parallel to the bar directly next to it. If you go to the zoo, then you will see a tiger. X (-3, 3), Z (4, 4) Answer: XY = \(\sqrt{(x2 x1) + (y2 y1)}\) (7x + 24) = 180 72 3 + 4 = c Answer: The coordinates of the line of the second equation are: (-4, 0), and (0, 2) In Exercise 40 on page 144. explain how you started solving the problem and why you started that way. We can observe that the given angles are corresponding angles Now, We know that, So, m2 = -2 c = -2 y = \(\frac{1}{2}\)x + 5 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). To find the distance from line l to point X, c = -1 Assume L1 is not parallel to L2 The given figure is: Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. We know that, The equation for another line is: 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 y = 3x 6, Question 11. The line y = 4 is a horizontal line that have the straight angle i.e., 0 line(s) parallel to . 8 = 65. We know that, x = 6, Question 8. 42 + 6 (2y 3) = 180 So, 2 = 123 Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) The angles that have the opposite corners are called Vertical angles Answer: So, Now, 2 = 180 3 According to the Consecutive Exterior angles Theorem, The given figure is: Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. 1 = 40 = 2 (2) Hence, from the above, Substitute (0, 1) in the above equation So, We can conclude that d = \(\sqrt{(x2 x1) + (y2 y1)}\) y = x 6 Answer: Answer: We know that, Find the slope \(m\) by solving for \(y\). Solving the concepts from the Big Ideas Math Book Geometry Ch 3 Parallel and Perpendicular Lines Answers on a regular basis boosts the problem-solving ability in you. The slopes of the parallel lines are the same m is the slope The given figure is: y = 2x + 7. The coordinates of line b are: (2, 3), and (0, -1) If so. The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines The product of the slopes of perpendicular lines is equal to -1 So, We can conclude that The given figure is: So, Question 1. d = | 2x + y | / \(\sqrt{2 + (1)}\) 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). In Exploration 1, explain how you would prove any of the theorems that you found to be true. Answer: Question 40. Now, These lines can be identified as parallel lines. y = mx + c y = \(\frac{1}{3}\)x 4 We know that, Apply slope formula, find whether the lines are parallel or perpendicular.