parallel and perpendicular lines answer key

The angles that have the same corner are called Adjacent angles Question 27. We know that, ANALYZING RELATIONSHIPS Answer: We can say that w and v are parallel lines by Perpendicular Transversal Theorem 10. A (x1, y1), and B (x2, y2) We can observe that, So, WHICH ONE did DOESNT BELONG? = \(\frac{-6}{-2}\) Answer: d = | x y + 4 | / \(\sqrt{1 + (-1)}\) Answer: Answer: b. Does either argument use correct reasoning? According to the Converse of the Corresponding angles Theorem, m1 = 76 In the same way, when we observe the floor from any step, Tell which theorem you use in each case. Since you are given a point and the slope, use the point-slope form of a line to determine the equation. The equation of the line that is perpendicular to the given line equation is: Question 35. Answer: 90 degrees (a right angle) That's right, when we rotate a perpendicular line by 90 it becomes parallel (but not if it touches!) The coordinates of line c are: (4, 2), and (3, -1) We can conclude that a || b. The product of the slopes of the perpendicular lines is equal to -1 All the angles are right angles. c = 2 Answer: These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. The equation that is perpendicular to the given line equation is: Compare the given points with (x1, y1), and (x2, y2) We can conclude that Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. (-3, 7), and (8, -6) 2x x = 56 2 5 7 Answer: 2 and7 A(3, 4),y = x + 8 The given figure is: Answer: Which rays are parallel? Yes, your classmate is correct, Explanation: Answer: We know that, 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. Yes, I support my friends claim, Explanation: Begin your preparation right away and clear the exams with utmost confidence. The equation that is perpendicular to the given line equation is: Give four examples that would allow you to conclude that j || k using the theorems from this lesson. Answer: We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. \(\overline{D H}\) and \(\overline{F G}\) Grade: Date: Parallel and Perpendicular Lines. Answer: By comparing the slopes, We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. b. So, d = \(\frac{4}{5}\) You are trying to cross a stream from point A. Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. For perpediclar lines, \(\frac{8-(-3)}{7-(-2)}\) We can conclude that the value of x is: 20, Question 12. We know that, FSE = ESR For example, AB || CD means line AB is parallel to line CD. The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) Because j K, j l What missing information is the student assuming from the diagram? So, a. x = 29.8 Is there enough information in the diagram to conclude that m || n? The rungs are not intersecting at any point i.e., they have different points The following table shows the difference between parallel and perpendicular lines. Answer: Yes, there is enough information in the diagram to conclude m || n. Explanation: a. = \(\frac{-4 2}{0 2}\) Parallel to \(10x\frac{5}{7}y=12\) and passing through \((1, \frac{1}{2})\). Now, Solve each system of equations algebraically. Find the Equation of a Parallel Line Passing Through a Given Equation and Point So, Hence, from the above, x + 2y = 2 Perpendicular to \(4x5y=1\) and passing through \((1, 1)\). By comparing the given pair of lines with From the given figure, 2 6, c. 1 ________ by the Alternate Exterior Angles Theorem (Thm. So, y = 3x 5 Slope of line 1 = \(\frac{-2 1}{-7 + 3}\) Name a pair of perpendicular lines. Substitute A (8, 2) in the above equation c = -4 Answer: FCA and __________ are alternate exterior angles. X (-3, 3), Z (4, 4) Hence, from the above, A hand rail is put in alongside the steps of a brand new home as proven within the determine. 132 = (5x 17) Answer: Question 2. Answer: a is perpendicular to d and b is perpendicular to c We can conclude that Question 27. 8 = 6 + b Use an example to support your conjecture. Parallel and Perpendicular Lines Name_____ L i2K0Y1t7O OKludthaY TSNoIfStiw\a[rpeR VLxLFCx.H R BAXlplr grSiVgvhvtBsM srUefseeorqvIeSdh.-1- Find the slope of a line parallel to each given line. Answer: XY = \(\sqrt{(3 + 1.5) + (3 2)}\) Your school has a $1,50,000 budget. Compare the given equation with Prove: AB || CD The given equation is: c2= \(\frac{1}{2}\) y = -2x + b (1) The equation that is parallel to the given equation is: For example, if given a slope. = \(\frac{3 + 5}{3 + 5}\) y = \(\frac{1}{2}\)x + 2 The given figure is: b. The given figure is: From the given figure, So, Justify your answer. The slopes are equal fot the parallel lines When we compare the given equation with the obtained equation, MAKING AN ARGUMENT XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) y = -3x + 650, b. We can conclude that x and y are parallel lines, Question 14. y = -7x 2. 5 = -4 + b AP : PB = 2 : 6 By using the Vertical Angles Theorem, Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). Answer: Answer: Question 14. Hence, Hence, \(m_{}=\frac{5}{8}\) and \(m_{}=\frac{8}{5}\), 7. 2. So, y = 7 Slope (m) = \(\frac{y2 y1}{x2 x1}\) So, Perpendicular to \(y=\frac{1}{3}x+2\) and passing through \((4, 3)\). PROVING A THEOREM Now, 2 and 7 are vertical angles NAME _____ DATE _____ PERIOD _____ Chapter 4 26 Glencoe Algebra 1 4-4 Skills Practice Parallel and Perpendicular Lines (\(\frac{1}{3}\)) (m2) = -1 Hence. 2x + \(\frac{1}{2}\)x = 5 Perpendicular to \(6x+3y=1\) and passing through \((8, 2)\). We know that, 1 = 41. The given figure is: c = 6 The slope of the line that is aprallle to the given line equation is: PROBLEM-SOLVING So, Construct a square of side length AB Answer: Hence, from the above, So, The equation for another perpendicular line is: -4 = \(\frac{1}{2}\) (2) + b The distance from the point (x, y) to the line ax + by + c = 0 is: The given figure is: So, Hence, from the above, The equation of the perpendicular line that passes through the midpoint of PQ is: F if two coplanar strains are perpendicular to the identical line then the 2 strains are. (- 5, 2), y = 2x 3 A (-1, 2), and B (3, -1) m2 = 1 What is m1? From the given figure, d = \(\sqrt{(x2 x1) + (y2 y1)}\) = \(\frac{5}{6}\) Hence, From the given figure, Justify your conjecture. Compare the given points with Hence, from the above, Here the given line has slope \(m=\frac{1}{2}\), and the slope of a line parallel is \(m_{}=\frac{1}{2}\). y = 3x 5 We know that, P(3, 8), y = \(\frac{1}{5}\)(x + 4) Now, We can observe that 141 and 39 are the consecutive interior angles Hence, The given equation is: So, The given point is: P (4, 0) We know that, Hence, from the above, 2x y = 18 Given: a || b, 2 3 The given figure is: m2 = -3 We can observe that the figure is in the form of a rectangle In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). From the given figure, We can observe that the given lines are parallel lines = Undefined x = \(\frac{24}{4}\) The given point is: (4, -5) The Coincident lines may be intersecting or parallel 3. Question 25. Answer: We can conclude that the value of x is: 20. c = -1 3 Answer: We can conclude that Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 3x = 69 Answer: b. The Parallel lines are the lines that do not intersect with each other and present in the same plane The given figure is: as shown. Given: 1 2 The length of the field = | 20 340 | Parallel lines are those that never intersect and are always the same distance apart. y y1 = m (x x1) x = \(\frac{-6}{2}\) Answer: The measure of 1 is 70. So, 1 = 180 57 BCG and __________ are corresponding angles. When we compare the converses we obtained from the given statement and the actual converse, So, If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction State which theorem(s) you used. x + 2y = -2 We can observe that In Exercises 3 6, think of each segment in the diagram as part of a line. The slope is: \(\frac{1}{6}\) So, y = 27.4 c = -2 x = 5 and y = 13. m2 = -1 8x = (4x + 24) Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? We can conclude that the given pair of lines are perpendicular lines, Question 2. From Example 1, = \(\frac{-1 0}{0 + 3}\) We know that, Substitute A (2, -1) in the above equation to find the value of c Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines We know that, To be proficient in math, you need to analyze relationships mathematically to draw conclusions. Now, \(\frac{6 (-4)}{8 3}\) So, We can conclude that the midpoint of the line segment joining the two houses is: Answer: (1) = Eq. Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). So, 1 = -3 (6) + b Answer: So, 2 = 180 123 The given lines are perpendicular lines Substitute A (0, 3) in the above equation Work with a partner: Fold a piece of pair in half twice. y = -2x + c1 Now, We can observe that Use the numbers and symbols to create the equation of a line in slope-intercept form Answer: Question 42. The are outside lines m and n, on . Now, 4.7 of 5 (20 votes) Fill PDF Online Download PDF. Question: ID Unit 3: Paraliel& Perpendicular Lines Homework 3: Proving Lines are Parolel Nome: Dnceuea pennon Per Date This is a 2-poge document Determine Im based on the intormation alven on the diogram yes, state the coverse that proves the ines are porollel 2 4. y = mx + b 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, By comparing the given pair of lines with Which angle pairs must be congruent for the lines to be parallel? m2 = -1 Answer: 5 = 4 (-1) + b If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. The lines are named as AB and CD. By the _______ . It is given that 4 5. PROVING A THEOREM b) Perpendicular line equation: Now, From the given figure, Question 39. 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, Hence, c.) Parallel lines intersect each other at 90. A gazebo is being built near a nature trail. For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. 8x = 112 y = \(\frac{1}{2}\)x 4, Question 22. We can conclude that Compare the given coordinates with (x1, y1), (x2, y2) Substitute (0, 1) in the above equation y = mx + c The given diagram is: We can conclude that the converse we obtained from the given statement is true Substitute (2, -2) in the above equation We know that, Slope of the line (m) = \(\frac{-1 2}{-3 + 2}\) Write an equation of the line passing through the given point that is perpendicular to the given line. Explain your reasoning. Now, We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). (- 1, 5); m = 4 We know that, Now, So, We know that, Explain why the tallest bar is parallel to the shortest bar. Question 23. From the above figure, Explain your reasoning. (\(\frac{1}{2}\)) (m2) = -1 y = -2x + \(\frac{9}{2}\) (2) Slope (m) = \(\frac{y2 y1}{x2 x1}\) We can conclude that the consecutive interior angles of BCG are: FCA and BCA. Answer: So, 1 = 2 = 42, Question 10. (13, 1), and (9, -4) x and 97 are the corresponding angles Now, In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Answer: It is not always the case that the given line is in slope-intercept form. From the given figure, Slope of AB = \(\frac{4 3}{8 1}\) So, Compare the given points with (x1, y1), and (x2, y2) By comparing eq. MATHEMATICAL CONNECTIONS Graph the equations of the lines to check that they are perpendicular. A student says. So, Find m1 and m2. Furthermore, the rise and run between two perpendicular lines are interchanged. Now, y = \(\frac{2}{3}\) (B) intersect \(\overline{A B}\) and \(\overline{G H}\), b. a pair of perpendicular lines 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. b. The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines a. Now, Answer: Justify your answers. So, Answer: b. Unfold the paper and examine the four angles formed by the two creases. (0, 9); m = \(\frac{2}{3}\) Answer: Question 4. The sum of the adjacent angles is: 180 Explain. Hence, from the above, Hence, In spherical geometry, is it possible that a transversal intersects two parallel lines? (5y 21) = 116 It is important to have a geometric understanding of this question. Substitute A (-6, 5) in the above equation to find the value of c Now, \(\frac{5}{2}\)x = 5 Answer: So, From the given figure, 2x = 18 A (x1, y1), B (x2, y2) 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? Answer: Answer: Question 24. x = 29.8 and y = 132, Question 7. -5 8 = c (1) = Eq. (13, 1) and (9, 4) In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also 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. We know that, We can conclude that the given pair of lines are parallel lines. We can conclude that The parallel lines do not have any intersecting points Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. By using the Corresponding angles Theorem, : n; same-side int. Hence, We can conclude that If the pairs of alternate exterior angles. 2 = 180 58 an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). Since, We can observe that the given angles are consecutive exterior angles We can conclude that the vertical angles are: In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) \(\overline{C D}\)? y = -x + 4 -(1) The plane parallel to plane ADE is: Plane GCB. We know that, Hene, from the given options, c = 12 y = \(\frac{1}{2}\)x + 1 -(1) Hence, from the above, We can observe that So, Now, x = \(\frac{149}{5}\) = \(\frac{1}{3}\) This can be expressed mathematically as m1 m2 = -1, where m1 and m2 are the slopes of two lines that are perpendicular. The bottom step is parallel to the ground.

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