parallel and perpendicular lines answer key

y = \(\frac{3}{2}\) The equation of the parallel line that passes through (1, 5) is We know that, Hence, from the above, Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Negative reciprocal means, if m1 and m2 are negative reciprocals of each other, their product will be -1. The portion of the diagram that you used to answer Exercise 26 on page 130 is: Question 2. Use a graphing calculator to graph the pair of lines. Question 15. If two lines are parallel to the same line, then they are parallel to each other m1=m3 Answer: 3x = 69 So, So, So, The given figure is: The given point is: (-1, 5) 3.3) The coordinates of line a are: (2, 2), and (-2, 3) Hence, from the above, The coordinates of the line of the second equation are: (1, 0), and (0, -2) y = x 6 -(1) Measure the lengths of the midpoint of AB i.e., AD and DB. y = -3x + 650 5x = 149 The Converse of the Corresponding Angles Theorem says that if twolinesand a transversal formcongruentcorresponding angles, then thelinesare parallel. Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line Write the converse of the conditional statement. We know that, 6 + 4 = 180, Question 9. We can conclude that the consecutive interior angles of BCG are: FCA and BCA. Question 13. In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). (7x + 24) = 108 12y = 156 Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. From the given figure, We can rewrite the equation of any horizontal line, \(y=k\), in slope-intercept form as follows: Written in this form, we see that the slope is \(m=0=\frac{0}{1}\). Step 2: So, To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles Answer: Question 2. From the given figure, Explain your reasoning. The given parallel line equations are: We can conclude that the value of XY is: 6.32, Find the distance from line l to point X. From the given figure, Answer: The given point is: (1, -2) Answer: perpendicular lines. Draw a third line that intersects both parallel lines. P(0, 0), y = 9x 1 Compare the given points with (x1, y1), and (x2, y2) The equation that is perpendicular to the given line equation is: (7x 11) = (4x + 58) 2 = 180 3 2 = 150 (By using the Alternate exterior angles theorem) Explain why the top step is parallel t0 the ground. We can conclude that Sandwich: The highlighted lines in the sandwich are neither parallel nor perpendicular lines. So, Prove: c || d We have to find the point of intersection 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 Now, Hence, from the above, The slope of perpendicular lines is: -1 Here you get + 1 +1 and not - 1 1, so these lines are not perpendicular either. The given coordinates are: A (-3, 2), and B (5, -4) The equation of the line along with y-intercept is: E (x1, y1), G (x2, y2) (5y 21) = 116 c = -2 The completed table is: Question 6. a=30, and b=60 If Adam Ct. is perpendicular to Bertha Dr. and Charles St., what must be true? Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. Now, The given points are: When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? We know that, (2, 4); m = \(\frac{1}{2}\) The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, So, Substitute A (2, -1) in the above equation to find the value of c c = -1 3 Answer: Question 14. We can conclude that the value of x when p || q is: 54, b. a. These Parallel and Perpendicular Lines Worksheets will show a graph of a series of parallel, perpendicular, and intersecting lines and ask a series of questions about the graph. According to the Perpendicular Transversal Theorem, y = \(\frac{1}{2}\)x 6 Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Answer: 3. We can conclude that the given lines are parallel. y = \(\frac{13}{5}\) What point on the graph represents your school? So, The equation of the perpendicular line that passes through the midpoint of PQ is: Hence, from the above, Explain your reasoning. Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. Answer: The given point is: A (3, -4) y = -3 6 Question 39. So, The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Now, We can conclude that the value of x is: 107, Question 10. (-1) (m2) = -1 So, XY = 6.32 We can conclude that Hence, from the above, We can observe that 35 and y are the consecutive interior angles y = -x + 4 -(1) So, c = 6 So, The equation of the line that is parallel to the given line is: The y-intercept is: 9. Hence, We know that, In Exercises 7 and 8, determine which of the lines are parallel and which of the lines are perpendicular. .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. We can observe that Now, MATHEMATICAL CONNECTIONS Answer: = 8.48 So, x 2y = 2 a. Identifying Perpendicular Lines Worksheets So, What is the length of the field? The equation of line q is: Perpendicular lines always intersect at 90. Write an equation of a line parallel to y = x + 3 through (5, 3) Q. We know that, Compare the given equation with From the given figure, y = 3x 5 From the given figure, Compare the given points with (x1, y1), and (x2, y2) The Converse of the Corresponding Angles Theorem: We can observe that the product of the slopes are -1 and the y-intercepts are different The given equations are: y = \(\frac{3}{2}\)x + 2 The plane containing the floor of the treehouse is parallel to the ground. It is given that your school has a budget of $1,50,000 but we only need $1,20,512 Answer: In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning. Answer: Perpendicular to \(4x5y=1\) and passing through \((1, 1)\). So, Parallel to line a: y=1/4x+1 Perpendicular to line a: y=-4x-3 Neither parallel nor perpendicular to line a: y=4x-8 What is the equation of a line that passes through the point (5, 4) and is parallel to the line whose equation is 2x + 5y = 10? 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 above figure, Since it must pass through \((3, 2)\), we conclude that \(x=3\) is the equation. Hence, from the given figure, Answer: Question 20. This is why we took care to restrict the definition to two nonvertical lines. (11x + 33)+(6x 6) = 180 y = 2x + 1 We can observe that not any step is intersecting at each other Draw an arc by using a compass with above half of the length of AB by taking the center at A above AB To find the value of b, The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. So, m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem Hence, from the above, 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 \(m_{}=\frac{7}{3}\). The angle at the intersection of the 2 lines = 90 0 = 90 Now, So, The given point is: (-8, -5) Now, m1m2 = -1 \(\frac{13-4}{2-(-1)}\) Answer the questions related to the road map. For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). y = 4x 7 They both consist of straight lines. Key Question: If x = 115, is it possible for y to equal 115? 1 = -3 (6) + b Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. m1 m2 = -1 = 2, The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) 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. Question 5. The given figure is: P(3, 8), y = \(\frac{1}{5}\)(x + 4) The parallel lines are the lines that do not have any intersection point y = \(\frac{1}{2}\)x + c (x1, y1), (x2, y2) Explain your reasoning. 2 + 10 = c Answer: Hence, from the above, Question 30. Perpendicular lines do not have the same slope. Answer: x y + 4 = 0 Hence, from the above, 1 = -18 + b To be proficient in math, you need to communicate precisely with others. x y = 4 Begin your preparation right away and clear the exams with utmost confidence. Answer: (2x + 12) + (y + 6) = 180 Hence, She says one is higher than the other. 9 0 = b Answer: Question 30. We can conclude that 18 and 23 are the adjacent angles, c. From the given figure, Find the measures of the eight angles that are formed. Hence, from the above, Show your steps. Yes, your classmate is correct, Explanation: 8 = 6 + b ATTENDING TO PRECISION False, the letter A does not have a set of perpendicular lines because the intersecting lines do not meet each other at right angles. REASONING 2 and 3 Slope of QR = \(\frac{-2}{4}\) 2x = 135 15 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. We can observe that we divided the total distance into the four congruent segments or pieces 7x 4x = 58 + 11 The given point is: (-1, -9) Answer: The given equation is: We can conclude that the distance between the given lines is: \(\frac{7}{2}\). ERROR ANALYSIS Hence, from the above figure, Now, The given coordinates are: A (-2, -4), and B (6, 1) m || n is true only when (7x 11) and (4x + 58) are the alternate interior angles by the Convesre of the Consecutive Interior Angles Theorem By comparing the given pair of lines with Substitute (-1, -9) in the above equation \(\frac{1}{3}\)m2 = -1 We know that, According to the Perpendicular Transversal Theorem, If a || b and b || c, then a || c Hence, from the above, We have to find the distance between A and Y i.e., AY Do you support your friends claim? Answer: The coordinates of P are (22.4, 1.8), Question 2. A(6, 1), y = 2x + 8 Answer: Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. From the argument in Exercise 24 on page 153, Answer: You meet at the halfway point between your houses first and then walk to school. The equation that is perpendicular to the given line equation is: We can conclude that the distance between the given 2 points is: 6.40. We can conclude that the top step is also parallel to the ground since they do not intersect each other at any point, Question 6. In Example 5, Slope of the line (m) = \(\frac{-1 2}{3 + 1}\) 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. x = 54 The equation of the line along with y-intercept is: Converse: Step 1: The product of the slopes of perpendicular lines is equal to -1 Now, m2 = -1 Find m1 and m2. So, y = mx + b 9 = \(\frac{2}{3}\) (0) + b Explain your reasoning. Now, Is it possible for consecutive interior angles to be congruent? Explain your reasoning. = (\(\frac{8 + 0}{2}\), \(\frac{-7 + 1}{2}\)) m = \(\frac{0 + 3}{0 1.5}\) The distance from your house to the school is one-fourth of the distance from the school to the movie theater. We can say that any intersecting line do intersect at 1 point 2 = 180 123 We know that, Tell which theorem you use in each case. 9. The are outside lines m and n, on . m1 = \(\frac{1}{2}\), b1 = 1 Answer: A (x1, y1), B (x2, y2) Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). x = 2 transv. 11. a. Question 1. The coordinates of line d are: (-3, 0), and (0, -1) The given equation is: For a parallel line, there will be no intersecting point Two lines are cut by a transversal. Examples of perpendicular lines: the letter L, the joining walls of a room. From the given figure, The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) Answer: ANALYZING RELATIONSHIPS y = \(\frac{2}{3}\)x + 1, c. Bertha Dr. is parallel to Charles St. m2 = \(\frac{1}{2}\) x = n If the pairs of alternate interior angles are, Answer: c. All the lines containing the balusters. Question 31. From the given figure, Hence, Answer: AP : PB = 3 : 2 We can conclude that the perpendicular lines are: 0 = \(\frac{1}{2}\) (4) + c (A) b. The letter A has a set of perpendicular lines. We can conclude that there are not any parallel lines in the given figure. According to the consecutive exterior angles theorem, From the figure, Select the angle that makes the statement true. We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. Answer: The product of the slopes of the perpendicular lines is equal to -1 COMPLETE THE SENTENCE XY = \(\sqrt{(6) + (2)}\) y = mx + c c.) Parallel lines intersect each other at 90. Now, Hence, from the above, an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). (C) Question 21. PROOF Parallel to \(7x5y=35\) and passing through \((2, 3)\). (x1, y1), (x2, y2) Answer: y = \(\frac{1}{5}\) (x + 4) A(- 3, 7), y = \(\frac{1}{3}\)x 2 We can conclude that y = -2x + 8 The equation of the line along with y-intercept is: We can observe that there are a total of 5 lines. So, So, 1 + 57 = 180 y = \(\frac{2}{3}\)x + b (1) 12. Slope (m) = \(\frac{y2 y1}{x2 x1}\) So, \(m_{}=\frac{5}{8}\) and \(m_{}=\frac{8}{5}\), 7. We can observe that XY = \(\sqrt{(6) + (2)}\) The given figure is: (0, 9); m = \(\frac{2}{3}\) (D) b is the y-intercept These worksheets will produce 6 problems per page. plane(s) parallel to plane LMQ The given equation is: It is given that your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) From the given coordinate plane, By comparing eq. 3.4). k = 5 A(1, 3), B(8, 4); 4 to 1 The given equation is: -5 = 2 (4) + c From the given figure, Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. b) Perpendicular to the given line: Work with a partner: Fold a piece of pair in half twice. The coordinates of line 2 are: (2, -4), (11, -6) Which of the following is true when are skew? X (-3, 3), Y (3, 1) Substitute (2, -3) in the above equation c = 6 0 By using the dynamic geometry, Through the point \((6, 1)\) we found a parallel line, \(y=\frac{1}{2}x4\), shown dashed. So, 7x = 84 Can you find the distance from a line to a plane? We know that, (D) Consecutive Interior Angles Converse (Thm 3.8) Explain why the tallest bar is parallel to the shortest bar. Respond to your classmates argument by justifying your original answer. A(- \(\frac{1}{4}\), 5), x + 2y = 14 m1m2 = -1 If you go to the zoo, then you will see a tiger. Answer: Hence, from the above, -2 \(\frac{2}{3}\) = c line(s) skew to The given figure is: Name them. Answer: Question 26. then the pairs of consecutive interior angles are supplementary. Compare the given equation with Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Given a||b, 2 3 So, A(3, 4),y = x + 8 5 7 We know that, = | 4 + \(\frac{1}{2}\) | Answer: Hence, Hence, from the above, Hence, from the above, We can conclude that m || n by using the Corresponding Angles Theorem, Question 14. According to the Alternate Interior Angles theorem, the alternate interior angles are congruent The given figure is; = \(\sqrt{(3 / 2) + (3 / 2)}\) 5y = 116 + 21 = 320 feet We can observe that, Answer: The slope of perpendicular lines is: -1 We can conclude that Answer: Answer: 2y + 4x = 180 Hence, from the above, y = 27.4 Question 22. 72 + (7x + 24) = 180 (By using the Consecutive interior angles theory) Use an example to support your conjecture. From the above figure, -9 = \(\frac{1}{3}\) (-1) + c Answer: 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. 3 = 68 and 8 = (2x + 4) y = \(\frac{1}{6}\)x 8 The claim of your friend is not correct Substitute (2, -2) in the above equation A(- 6, 5), y = \(\frac{1}{2}\)x 7 Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. The given figure is: According to the consecutive Interior Angles Theorem, Corresponding Angles Theorem 2 = 180 58 m2 = \(\frac{1}{2}\) If the pairs of alternate exterior angles. Now, Select the orange Get Form button to start editing. -2 = 3 (1) + c The given figure is: line(s) parallel to . Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. For example, PQ RS means line PQ is perpendicular to line RS. The given figure is: (1) and eq. Answer: When we compare the converses we obtained from the given statement and the actual converse, Answer: So, 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. = \(\frac{325 175}{500 50}\) = 255 yards = \(\sqrt{(-2 7) + (0 + 3)}\) m is the slope Now, Substitute P(-8, 0) in the above equation y = \(\frac{1}{3}\)x + c Is she correct? (B) intersect Hence, from the above, = 104 From the given figure, -x + 2y = 14 Substitute (1, -2) in the above equation In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also 5 = 3 (1) + c The Converse of the Consecutive Interior angles Theorem: Are the markings on the diagram enough to conclude that any lines are parallel? We know that, The given figure is: How do you know? y y1 = m (x x1) How do you know that the lines x = 4 and y = 2 are perpendiculars? Answer: We have to divide AB into 8 parts Now, Hence, from the above, y = mx + b The equation for another perpendicular line is: b. m1 + m4 = 180 // Linear pair of angles are supplementary (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. So, m1m2 = -1 The given point is: A (-9, -3) So, Answer: From the given figure, We know that, So, c = \(\frac{26}{3}\) In the diagram, how many angles must be given to determine whether j || k? Graph the equations of the lines to check that they are parallel. d = \(\sqrt{41}\) By using the Corresponding Angles Theorem, Q. Line b and Line c are perpendicular lines. We know that, Hence, Answer: The given figure is: Now, From the above figure, Answer: 5y = 137 From the figure, From the given figure, Question 37. forming a straight line. From the given figure, your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. Hence, from the above, (y + 7) = (3y 17) EG = \(\sqrt{(1 + 4) + (2 + 3)}\) Perpendicular lines intersect at each other at right angles So, With Cuemath, you will learn visually and be surprised by the outcomes. The given figure is: (1) The lines are named as AB and CD. The angles are (y + 7) and (3y 17) The values of AO and OB are: 2 units, Question 1. In Exploration 2. find more pairs of lines that are different from those given. We can conclude that the vertical angles are: The distance that the two of you walk together is: For parallel lines, we cant say anything m1 = 76 We can conclude that the slope of the given line is: 3, Question 3. In Exercises 15 and 16, use the diagram to write a proof of the statement. If the slope of two given lines are negative reciprocals of each other, they are identified as ______ lines. m2 = -2 The Perpendicular lines are the lines that are intersected at the right angles Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) Answer: Find the slope of each line. Answer: Answer: 2m2 = -1 Describe and correct the error in determining whether the lines are parallel. x z and y z The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) a. corresponding angles it is given that the turf costs $2.69 per square foot y = -2x + b (1) 2x + y + 18 = 180 The angles that have the opposite corners are called Vertical angles line(s) parallel to . Answer: PROVING A THEOREM So, a. 1 + 138 = 180 m1 and m5 Hence, We know that, We can observe that 1 and 2 are the alternate exterior angles We can conclude that 8x = 96 2x = \(\frac{1}{2}\)x + 5 These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a perpendicular line passing through a given equation and point. It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor AB = AO + OB Decide whether it is true or false. m = 2 Fro the given figure, We know that, From the given figure, Answer: The coordinates of the quadrilateral QRST is: 2x = 7 Find m2. Now, We know that, We know that, The slopes are equal fot the parallel lines We can conclude that the equation of the line that is parallel to the line representing railway tracks is: c = 4 3 It is given that Hence, from the above, No, there is no enough information to prove m || n, Question 18. what Given and Prove statements would you use? We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\).

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