Select all that apply. Here is a quick review of the point/slope form of a line. 1 + 2 = 180 Now, The given point is: (6, 1) (1) Q (2, 6), R (6, 4), S (5, 1), and T (1, 3) We can conclude that y = -3x + 650 We know that, 3 (y 175) = x 50 Question 13. The area of the field = Length Width Perpendicular to \(x+7=0\) and passing through \((5, 10)\). 2 = 123 Now, Answer: Substitute (4, -3) in the above equation y = x 6 -(1) Answer: Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. We know that, From the given figure, y = \(\frac{2}{3}\) The two lines are Intersecting when they intersect each other and are coplanar Prove: c || d From the construction of a square in Exercise 29 on page 154, We can observe that 12. Line 2: (2, 4), (11, 6) Compare the given equation with We know that, According to the Converse of the Corresponding angles Theorem, If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. So, = \(\frac{9}{2}\) Hence, from the above, The slopes are equal fot the parallel lines Answer: 8x and 96 are the alternate interior angles The equation of a line is: Compare the given points with (x1, y1), and (x2, y2) Parallel lines are those that never intersect and are always the same distance apart. y = -3 (0) 2 Point A is perpendicular to Point C If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles We can conclude that the value of k is: 5. -x + 2y = 14 The coordinates of line c are: (2, 4), and (0, -2) Answer: 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. 1 = 40 y = 2x + 3, Question 23. \(\begin{array}{cc} {\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(-1,-5)}&{m_{\perp}=4}\end{array}\). The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent c = 5 y = -3x + 650, b. Given: k || l By using the Consecutive interior angles Theorem, 1 = 2 = 150, Question 6. We know that, We know that, Given: 1 and 3 are supplementary From the given figure, Perpendicular lines have slopes that are opposite reciprocals. We know that, Answer: w y and z x We can observe that not any step is intersecting at each other Section 6.3 Equations in Parallel/Perpendicular Form. Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2). Answer: x = -3 d = \(\sqrt{(x2 x1) + (y2 y1)}\) From the given figure, 12y 18 = 138 a. Answer: Question 26. Answer: Question 26. 5y = 137 To use the "Parallel and Perpendicular Lines Worksheet (with Answer Key)" use the clues in identifying whether two lines are parallel or perpendicular with each other using the slope. The given point is: A (3, -4) y = -x + 8 Question 7. Compare the given coordinates with (x1, y1), and (x2, y2) The given points are: The given figure is: ATTENDING TO PRECISION Answer: The coordinates of the meeting point are: (150, 200) So, Substitute (-1, 6) in the above equation The parallel line equation that is parallel to the given equation is: Which is different? Question 1. We can conclude that Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are parallel if their slopes are the same, \(m_{1}=m_{2}\). Draw the portion of the diagram that you used to answer Exercise 26 on page 130. y = 4x 7 x + 2y = 10 2x + 4y = 4 Compare the given points with We know that, c = 8 \(\frac{3}{5}\) y = \(\frac{1}{2}\)x + b (1) How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? d = 32 So, (2) We know that, The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel lines from pictures. Answer: Given: k || l, t k So, Substitute (-5, 2) in the given equation = \(\frac{2}{9}\) y = \(\frac{1}{3}\)x + c Fro the given figure, So, 2 = 122 2. We can conclude that the value of x is: 20. c = 0 We know that, So, The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. y = \(\frac{1}{5}\) (x + 4) A(2, 1), y = x + 4 We know that, ABSTRACT REASONING justify your answer. The equation of the parallel line that passes through (1, 5) is y = 3x + 2, (b) perpendicular to the line y = 3x 5. No, we did not name all the lines on the cube in parts (a) (c) except \(\overline{N Q}\). Now, 2x y = 18 Now, b = 19 Find equations of parallel and perpendicular lines. c. m5=m1 // (1), (2), transitive property of equality Now, So, Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) According to the Corresponding Angles Theorem, the corresponding angles are congruent The Converse of Corresponding Angles Theorem: Make a conjecture about what the solution(s) can tell you about whether the lines intersect. x = 2 m1m2 = -1 We can conclude that We know that, 11y = 77 These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. We know that, If two parallel lines are cut by a transversal, then the pairs of Alternate exterior angles are congruent. ERROR ANALYSIS Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. d. AB||CD // Converse of the Corresponding Angles Theorem. y = 4x + 9, Question 7. (11x + 33) and (6x 6) are the interior angles Hence, Question 25. So, PROOF For the intersection point of y = 2x, The slope of horizontal line (m) = 0 We can conclude that 1 = 60. Prove \(\overline{A B} \| \overline{C D}\) We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6. P = (7.8, 5) Question 23. Compare the given coordinates with The given equation is: So, MODELING WITH MATHEMATICS Answer: Our Parallel and Perpendicular Lines Worksheets are free to download, easy to use, and very flexible. So, The given figure is: Slope (m) = \(\frac{y2 y1}{x2 x1}\) In Example 4, the given theorem is Alternate interior angle theorem The given line equation is: The given point is: (-1, -9) Now, We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles From the given figure, So, Now, c. Consecutive Interior angles Theorem, Question 3. For parallel lines, 1 + 138 = 180 So, Hence, Hence, You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. y = -x + c If we draw the line perpendicular to the given horizontal line, the result is a vertical line. Parallel to \(6x\frac{3}{2}y=9\) and passing through \((\frac{1}{3}, \frac{2}{3})\). d = | 6 4 + 4 |/ \(\sqrt{2}\)} Answer: Question 29. Question 4. Parallel and perpendicular lines have one common characteristic between them. Find the distance front point A to the given line. y = \(\frac{1}{2}\)x 3, b. From the given figure, Question 22. We know that, In Exercises 9 and 10, trace \(\overline{A B}\). So, Answer: Answer: The standard form of the equation is: Slope of line 2 = \(\frac{4 + 1}{8 2}\) Hence, from the above, We know that, 5 = \(\frac{1}{2}\) (-6) + c Find the values of x and y. The given figure is: d = \(\sqrt{(x2 x1) + (y2 y1)}\) A (-1, 2), and B (3, -1) 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. MODELING WITH MATHEMATICS Hence, from the above, Hence, from the above, Then by the Transitive Property of Congruence (Theorem 2.2), _______ . y = 3x + 9 We know that, The equation that is parallel to the given equation is: So, Question 1. Hence, So, Which angle pairs must be congruent for the lines to be parallel? Answer: parallel Answer: Explanation: In the above image we can observe two parallel lines. x = 5 The bottom step is parallel to the ground. CONSTRUCTING VIABLE ARGUMENTS b.) Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. Now, Answer: They are not perpendicular because they are not intersecting at 90. y = \(\frac{1}{3}\)x 2 -(1) THOUGHT-PROVOKING 1 = 2 = 42, Question 10. The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: Now, Then, let's go back and fill in the theorems. From the given figure, 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. MATHEMATICAL CONNECTIONS 1 (m2) = -3 x = 29.8 and y = 132, Question 7. .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. as shown. The slope is: \(\frac{1}{6}\) The given figure is: (A) Corresponding Angles Converse (Thm 3.5) (B) intersect Find the equation of the line passing through \((3, 2)\) and perpendicular to \(y=4\). Find the equation of the line perpendicular to \(x3y=9\) and passing through \((\frac{1}{2}, 2)\). So, If two intersecting lines are perpendicular. The given equation is: Consider the following two lines: Consider their corresponding graphs: Figure 4.6.1 The given figure is: If you use the diagram below to prove the Alternate Exterior Angles Converse. (D) Consecutive Interior Angles Converse (Thm 3.8) 42 and 6(2y 3) are the consecutive interior angles m = 2 y = -3x 2 a. We know that, x = \(\frac{120}{2}\) d = | 2x + y | / \(\sqrt{2 + (1)}\) The equation for another perpendicular line is: Which type of line segment requires less paint? Compare the given equation with Let the given points are: 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. m = \(\frac{3 0}{0 + 1.5}\) 5 = 105, To find 8: 2x + y = 162(1) Now, What is the relationship between the slopes? m1m2 = -1 The given figure is: \(\frac{5}{2}\)x = 5 C(5, 0) 2 and 4 are the alternate interior angles which ones? If you were to construct a rectangle, Find the perpendicular line of y = 2x and find the intersection point of the two lines We can say that w and x are parallel lines by Perpendicular Transversal theorem. Answer: Question 17. Hence, = \(\sqrt{31.36 + 7.84}\) We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{1}{m_{2}}\). m1m2 = -1 Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. We know that, Eq. So, Write an equation of a line parallel to y = x + 3 through (5, 3) Q. (1) = Eq. Proof: Question 23. 12y = 156 y = \(\frac{1}{4}\)x + b (1) From the given bars, Legal. The given equation is: From the given figure, So, From Example 1, 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 Possible answer: 1 and 3 b. We can observe that So, We know that, From the given figure, 1) line(s) PerPendicular to . We can conclude that the third line does not need to be a transversal. Answer: b. Unfold the paper and examine the four angles formed by the two creases. Use the diagram We have to divide AB into 10 parts We can conclude that m || n by using the Corresponding Angles Theorem, Question 14. y = \(\frac{1}{3}\)x \(\frac{8}{3}\). The given figure is: We can observe that, In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m. Question 10. 10. Now, then they are parallel. MAKING AN ARGUMENT The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept XZ = \(\sqrt{(7) + (1)}\) Step 6: An equation of the line representing the nature trail is y = \(\frac{1}{3}\)x 4. 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. 1 and 8 are vertical angles Hence, from the above, m1 = \(\frac{1}{2}\), b1 = 1 Now, (C) Alternate Exterior Angles Converse (Thm 3.7) Classify each pair of angles whose measurements are given. m1 m2 = -1 In spherical geometry, all points are points on the surface of a sphere. y = \(\frac{1}{3}\)x + c If r and s are the parallel lines, then p and q are the transversals. The given point is: A (3, 4) Substitute A (0, 3) in the above equation Converse: c = -2 \(\overline{C D}\) and \(\overline{E F}\), d. a pair of congruent corresponding angles We can observe that 1 and 2 are the consecutive interior angles Eq. We can conclude that the linear pair of angles is: y = 0.66 feet (1) Write an equation of the line passing through the given point that is perpendicular to the given line. y = 4 x + 2 2. y = 5 - 2x 3. x = 14 Answer: We can conclude that the value of x when p || q is: 54, b. The distance that the two of you walk together is: y = 3x + 2 COMPLETE THE SENTENCE We can conclude that the given pair of lines are parallel lines. The perpendicular line equation of y = 2x is: The given figure is: Compare the given equation with plane(s) parallel to plane CDH The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) The equation that is perpendicular to the given equation is: The equation for another line is: We know that, y = \(\frac{13}{5}\) In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. b. m1 + m4 = 180 // Linear pair of angles are supplementary AP : PB = 4 : 1 We can conclude that the value of x is: 90, Question 8. XZ = \(\sqrt{(4 + 3) + (3 4)}\) Answer: A(3, 1), y = \(\frac{1}{3}\)x + 10 Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Answer: Question 52. We get Parallel to \(\frac{1}{5}x\frac{1}{3}y=2\) and passing through \((15, 6)\). Question 13. The coordinates of line 2 are: (2, -4), (11, -6) In Exercises 11-14, identify all pairs of angles of the given type. Hence, from the above figure, So, Substitute (4, -5) in the above equation y = x + 9 So, We know that, y = -2x + 2, Question 6. You are looking : parallel and perpendicular lines maze answer key pdf Contents 1. Describe and correct the error in the students reasoning We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. line(s) parallel to Find m1. Slope (m) = \(\frac{y2 y1}{x2 x1}\) The slopes are equal fot the parallel lines The given point is: P (-8, 0) 140 21 32 = 6x 1 = 2 Hence, from the above, This is why we took care to restrict the definition to two nonvertical lines. Hence, from he above, Perpendicular lines are intersecting lines that always meet at an angle of 90. Question 12. Compare the given equation with The slope of the line of the first equation is: Write an inequality for the slope of a line perpendicular to l. Explain your reasoning. d. AB||CD // Converse of the Corresponding Angles Theorem -4 1 = b We know that, P(4, 6)y = 3 So, So, Answer: -2 3 = c Answer: Answer: The given equation is: The plane parallel to plane ADE is: Plane GCB. The total cost of the turf = 44,800 2.69 Using P as the center, draw two arcs intersecting with line m. Hence, from the above, The coordinates of P are (22.4, 1.8), Question 2. So, When we compare the actual converse and the converse according to the given statement, Substitute (3, 4) in the above equation 4.7 of 5 (20 votes) Fill PDF Online Download PDF. Answer: = Undefined Now, alternate interior m2 = -3 a. y = 4x + 9 Can you find the distance from a line to a plane? The angles are (y + 7) and (3y 17) From the figure, From the above figure, Answer: The symbol || is used to represent parallel lines. x = \(\frac{96}{8}\) We can observe that the slopes are the same and the y-intercepts are different We can observe that Hence, from the above, We can conclude that the theorem student trying to use is the Perpendicular Transversal Theorem. Substitute the given point in eq. So, Answer: The given figure is: Select the angle that makes the statement true. 1 3, -4 = \(\frac{1}{2}\) (2) + b The given points are: The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) \(m_{}=4\) and \(m_{}=\frac{1}{4}\), 5. Answer: Substitute P (3, 8) in the above equation to find the value of c Draw a third line that intersects both parallel lines. So, Hence, (-1) (m2) = -1 \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. y = mx + c XY = \(\sqrt{(x2 x1) + (y2 y1)}\) x = 40 Hence, We can conclude that Hence, from the above,