parallel and perpendicular lines answer key

y = \(\frac{1}{2}\)x + c According to the Perpendicular Transversal Theorem, The angles that have the opposite corners are called Vertical angles 1 = 32. Answer: Question 34. The converse of the given statement is: Now, This no prep unit bundle will assist your college students perceive parallel strains and transversals, parallel and perpendicular strains proofs, and equations of parallel and perpendicular. Hence, from the above, How do you know that the lines x = 4 and y = 2 are perpendiculars? = 44,800 square feet \(\overline{D H}\) and \(\overline{F G}\) are Skew lines because they are not intersecting and are non coplanar, Question 1. 1 4. -2 \(\frac{2}{3}\) = c y = mx + c Answer: 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. Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). The given figure is: The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) By using the Perpendicular transversal theorem, R and s, parallel 4. Hence, from the above, According to this Postulate, The equation of the parallel line that passes through (1, 5) is From the given bars, Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. 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 Question 5. Answer: Question 24. Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. m = \(\frac{1}{4}\) So, These Parallel and Perpendicular Lines Worksheets will give the slope of a line and ask the student to determine the slope for any line that is parallel and the slope that is perpendicular to the given line. Substitute (-5, 2) in the above equation A(3, 6) We can observe that the given pairs of angles are consecutive interior angles Question 39. The equation for another perpendicular line is: So, Hence, She says one is higher than the other. Given: k || l, t k The given point is: A (2, 0) Hence, from the above, Draw an arc with center A on each side of AB. By using the Corresponding Angles Theorem, Converse: Hence, from the above, Are the numbered streets parallel to one another? c. m5=m1 // (1), (2), transitive property of equality We can conclude that the distance from point A to the given line is: 2.12, Question 26. The equation of the line along with y-intercept is: So, The Intersecting lines are the lines that intersect with each other and in the same plane The width of the field is: 140 feet Explain. The given pair of lines are: Compare the given equation with The equation for another parallel line is: c. Draw \(\overline{C D}\). MODELING WITH MATHEMATICS In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. The lines that have the same slope and different y-intercepts are Parallel lines So, We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction -x + 2y = 14 Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 Find the other angle measures. So, c = -3 Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3. We can observe that = 2 (2) The given figure is: y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) y = mx + c The slope of the given line is: m = \(\frac{2}{3}\) Draw a line segment of any length and name that line segment as AB P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. Yes, there is enough information to prove m || n Answer: The coordinates of line c are: (4, 2), and (3, -1) 4 and 5 are adjacent angles By comparing eq. d = | 2x + y | / \(\sqrt{2 + (1)}\) We can conclude that 1 2. the equation that is perpendicular to the given line equation is: Explain your reasoning. \(\frac{6-(-4)}{8-3}\) Hence, from the above, Transitive Property of Parallel Lines Theorem (Theorem 3.9),/+: If two lines are parallel to the same line, then they are parallel to each other. = \(\frac{-4}{-2}\) The given figure is: The slope of the given line is: m = \(\frac{1}{4}\) Hence, Describe how you would find the distance from a point to a plane. We can conclude that the distance from point A to the given line is: 1.67. Hence, Step 4: Find the distance from point E to We know that, Question 1. So, We can observe that x and 35 are the corresponding angles 2 = 180 123 So, The given figure is: From the Consecutive Exterior angles Converse, To find the coordinates of P, add slope to AP and PB XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We can observe that all the angles except 1 and 3 are the interior and exterior angles The given equation is: Answer: Now, The given figure is: = \(\frac{325 175}{500 50}\) PROBLEM-SOLVING The standard form of the equation is: y = \(\frac{1}{7}\)x + 4 We can conclude that So, The intersecting lines intersect each other and have different slopes and have the same y-intercept Answer: We know that, How would your x + x = -12 + 6 So, AC is not parallel to DF. y = \(\frac{1}{2}\)x + 2 y = 4x + b (1) So, y = 3x 6, Question 11. Find the equation of the line passing through \((3, 2)\) and perpendicular to \(y=4\). Let the two parallel lines that are parallel to the same line be G So, (b) perpendicular to the given line. c = -2 = Undefined The equation that is perpendicular to the given equation is: The converse of the Alternate Interior angles Theorem: By using the consecutive interior angles theorem, y = \(\frac{3}{2}\)x 1 MATHEMATICAL CONNECTIONS For the proofs of the theorems that you found to be true, refer to Exploration 1. Given a||b, 2 3 We can conclude that m and n are parallel lines, Question 16. a. y = -7x 2. A (x1, y1), and B (x2, y2) a is both perpendicular to b and c and b is parallel to c, Question 20. We know that, We know that, c.) False, parallel lines do not intersect each other at all, only perpendicular lines intersect at 90. Answer: A student says. The coordinates of line q are: y = -2x + 8 We know that, Answer: XY = \(\sqrt{(3 + 3) + (3 1)}\) Answer: Question 14. So, c = 8 Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) m1 and m5 5 = \(\frac{1}{2}\) (-6) + c x = -1 a. m5 + m4 = 180 //From the given statement So, 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. We can conclude that m1 m2 = \(\frac{1}{2}\) 2 4.5 Equations of Parallel and Perpendicular Lines Solving word questions = \(\sqrt{1 + 4}\) c. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. So, It is given that 4 5 and \(\overline{S E}\) bisects RSF A(3, 4),y = x + 8 Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets Question 7. Hence, from the above, Hence, m2 = \(\frac{1}{2}\) It is given that 1 = 58 Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. Answer: Answer: The given figure is: For example, if given a slope. XY = 4.60 Answer: Proof of the Converse of the Consecutive Interior angles Theorem: We know that, The claim of your friend is not correct c = 5 From the construction of a square in Exercise 29 on page 154, According to the Vertical Angles Theorem, the vertical angles are congruent = \(\sqrt{(6) + (6)}\) The given point is: A (3, 4) When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. According to the Corresponding Angles Theorem, the corresponding angles are congruent Answer: Equations of vertical lines look like \(x=k\). d = \(\sqrt{(x2 x1) + (y2 y1)}\) 2y and 58 are the alternate interior angles (E) Answer: P(2, 3), y 4 = 2(x + 3) So, p || q and q || r. Find m8. Answer: We know that, You and your friend walk to school together every day. \(m_{}=\frac{4}{3}\) and \(m_{}=\frac{3}{4}\), 15. c = -2 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 Answer: y = -3x + 650, b. b is the y-intercept y = 3x 5 y = -x 1, Question 18. Compare the given equation with 2 = 180 47 x = 9 Perpendicular lines meet at a right angle. Answer: Answer: A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). To find the distance from point X to \(\overline{W Z}\), Answer: Question 32. So, From the given figure, Hence, From Example 1, If you go to the zoo, then you will see a tiger A (x1, y1), B (x2, y2) The given figure is: So, The given figure is: Question 12. It is given that, y = \(\frac{137}{5}\) The sum of the given angle measures is: 180 So, WHICH ONE did DOESNT BELONG? The coordinates of the line of the second equation are: (-4, 0), and (0, 2) \(\frac{8-(-3)}{7-(-2)}\) The given coordinates are: A (-2, -4), and B (6, 1) We get 6 + 4 = 180, Question 9. Answer: y = \(\frac{1}{3}\)x + 10 Consecutive Interior Angles Converse (Theorem 3.8) x + 2y = 2 So, From the given figure, The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) We know that, The angles that have the common side are called Adjacent angles Now, Hence, from the above, d = 364.5 yards y = \(\frac{10 12}{3}\) m is the slope Which line(s) or plane(s) appear to fit the description? Prove the statement: If two lines are vertical. c = 5 + 3 Now, parallel Answer: Explanation: In the above image we can observe two parallel lines. Parallel lines are lines in the same plane that never intersect. Answer: 2 and 4 are the alternate interior angles We can conclude that x and y are parallel lines, Question 14. -x = x 3 Question 4. m2 = -2 8 = 105, Question 2. So, 8x and (4x + 24) are the alternate exterior angles PDF Solving Equations Involving Parallel and Perpendicular Lines Examples then they are parallel to each other. The following table shows the difference between parallel and perpendicular lines. According to the consecutive exterior angles theorem, The given rectangular prism of Exploration 2 is: Give four examples that would allow you to conclude that j || k using the theorems from this lesson. The lines that do not have any intersection points are called Parallel lines Question 35. = 2, The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) So, (4.3.1) - Parallel and Perpendicular Lines - Lumen Learning The Converse of the alternate exterior angles Theorem: Parallel lines are those that never intersect and are always the same distance apart. Hence, from the above, The equation that is perpendicular to the given line equation is: So, Identify two pairs of perpendicular lines. x = 3 (2) Draw a line segment CD by joining the arcs above and below AB The given figure is: Answer: We know that, m1m2 = -1 Answer: y = -2 c = \(\frac{40}{3}\) y = -2x + c1 Explain why the top step is parallel t0 the ground. Now, The lines that do not intersect or not parallel and non-coplanar are called Skew lines y = \(\frac{3}{2}\)x + 2, b. West Texas A&M University | WTAMU Notice that the slope is the same as the given line, but the \(y\)-intercept is different. = \(\frac{6}{2}\) The given line has slope \(m=\frac{1}{4}\), and thus \(m_{}=+\frac{4}{1}=4\). Answer: Question 26. If you were to construct a rectangle, Compare the above equation with = \(\frac{10}{5}\) Compare the given points with 2 6, c. 1 ________ by the Alternate Exterior Angles Theorem (Thm. k = 5 Answer: The representation of the given point in the coordinate plane is: Question 54. So, Substitute P (3, 8) in the above equation to find the value of c So, 4x y = 1 3y = x + 475 Explain Your reasoning. b. m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem m2 = -2 y = \(\frac{1}{3}\)x + c If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. CONSTRUCTING VIABLE ARGUMENTS Hence, from the above, If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. We can say that w and v are parallel lines by Perpendicular Transversal Theorem Slope of JK = \(\frac{n 0}{0 0}\) Let the congruent angle be P m is the slope Hence, from the above, PDF 3-7 Slopes of Parallel and Perpendicular Lines 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. From the argument in Exercise 24 on page 153, We can observe that 10x + 2y = 12 We know that, 1 = 180 140 In Exploration 2. m1 = 80. Where, So, x = y =29 a.) The given points are: Writing Equations Of Parallel And Perpendicular Lines Answer Key Kuta For a horizontal line, Answer: m1 m2 = -1 In Exercises 3 and 4. find the distance from point A to . What are Parallel and Perpendicular Lines? m1 m2 = -1 Get Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines For example, PQ RS means line PQ is perpendicular to line RS. Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope? Hence, from the above, Parallel to \(2x3y=6\) and passing through \((6, 2)\). Answer: y = mx + c Answer: Question 20. We can say that Find m2 and m3. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. EG = 7.07 So, (11y + 19) = 96 If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel y = \(\frac{1}{2}\)x + c Answer: Answer: The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) So, When two lines are crossed by another line (which is called the Transversal), theangles in matching corners are called Corresponding angles y = \(\frac{1}{3}\)x 4 Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). So, We know that, y = mx + c 1 5 Line 1: (10, 5), (- 8, 9) 200), d. What is the distance from the meeting point to the subway? We can conclude that We know that, Hence, All perpendicular lines can be termed as intersecting lines, but all intersecting lines cannot be called perpendicular because they need to intersect at right angles. = \(\frac{6 0}{0 + 2}\) Hence, from the above, 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. To find the coordinates of P, add slope to AP and PB Compare the given equation with = -3 a. Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. Answer: .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. Measure the lengths of the midpoint of AB i.e., AD and DB. Where, Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. Some examples follow. From the given figure, The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). We can observe that The Converse of the Alternate Exterior Angles Theorem: Construct a square of side length AB \(m_{}=\frac{2}{7}\) and \(m_{}=\frac{7}{2}\), 17. It is given that l || m and l || n, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) Answer: Step 5: c = 2 0 Question 4. 2x = 180 The coordinates of P are (3.9, 7.6), Question 3. Given 1 and 3 are supplementary. The angles are (y + 7) and (3y 17) Answer: Question 11. Hence, from the above, The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent If we observe 1 and 2, then they are alternate interior angles Hence, from the above, The lines that do not intersect to each other and are coplanar are called Parallel lines Proof of Alternate exterior angles Theorem: Answer: The given figure is: The equation that is parallel to the given equation is: Find both answers. A(2, 0), y = 3x 5 AO = OB x = y = 61, Question 2. HOW DO YOU SEE IT? Compare the given coordinates with c = -1 2 Question 4. (11x + 33) and (6x 6) are the interior angles Hence, from the above, Use the diagram could you still prove the theorem? X (-3, 3), Z (4, 4) We know that, c = 0 2 c = -12 d = \(\sqrt{41}\) line(s) perpendicular to Examples of parallel lines: Railway tracks, opposite sides of a whiteboard. Hence, from the above, -5 = 2 + b We know that, Question 13. In Exercises 11 and 12. prove the theorem. XY = \(\sqrt{(3 + 3) + (3 1)}\) The given figure is: So, Question 27. So, c = -1 1 Equations parallel and perpendicular lines answer key

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