The given point is: A (-3, 7) -2 . In Exploration 2. find more pairs of lines that are different from those given. The equation of a line is x + 2y = 10. One answer is the line that is parallel to the reference line and passing through a given point. The given equation is: P(- 7, 0), Q(1, 8) We can conclude that, We know that, Hence, from the above, Yes, there is enough information to prove m || n Hence, From the given figure, d = | 6 4 + 4 |/ \(\sqrt{2}\)} We can observe that So, 2 = 41 Hence, from the above, Write an equation of the line that passes through the point (1, 5) and is The given figure is: We can conclude that The equation of the line along with y-intercept is: We can observe that the given angles are consecutive exterior angles b.) So, Answer: The given equation is: From the given figure, The product of the slopes of perpendicular lines is equal to -1 We can observe that the given lines are perpendicular lines From the figure, First, solve for \(y\) and express the line in slope-intercept form. NAME _____ DATE _____ PERIOD _____ Chapter 4 26 Glencoe Algebra 1 4-4 Skills Practice Parallel and Perpendicular Lines 6 + 4 = 180, Question 9. y = \(\frac{3}{5}\)x \(\frac{6}{5}\) We know that, 1 and 5 are the alternate exterior angles Hence, from the above, So, Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. So, m = \(\frac{0 2}{7 k}\) Answer: The Converse of the alternate exterior angles Theorem: = 0 The standard linear equation is: In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. Answer: We can conclude that \(\frac{3}{2}\) . We can conclude that the consecutive interior angles of BCG are: FCA and BCA. b) Perpendicular to the given line: Hence, They are not perpendicular because they are not intersecting at 90. The coordinates of the line of the first equation are: (-1.5, 0), and (0, 3) The points of intersection of parallel lines: We know that, y = 180 48 The bottom step is parallel to the ground. The given point is: A (3, -1) 2y + 4x = 180 We know that, HOW DO YOU SEE IT? MATHEMATICAL CONNECTIONS What is the distance between the lines y = 2x and y = 2x + 5? \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). Solve each system of equations algebraically. We can conclude that 4x = 24 Answer: Question 2. We know that, So, We have to find the point of intersection The equation that is perpendicular to the given equation is: y = mx + c 2m2 = -1 y = \(\frac{1}{2}\)x + 5 Now, Slope of AB = \(\frac{4}{6}\) y = mx + c So, For a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1 = 180 76 P || L1 HOW DO YOU SEE IT? x = 40 It is given that We can conclude that the distance from point A to the given line is: 1.67. m || n is true only when 147 and (x + 14) are the corresponding angles by using the Converse of the Alternate Exterior Angles Theorem The line that passes through point F that appear skew to \(\overline{E H}\) is: \(\overline{F C}\), Question 2. ABSTRACT REASONING Question 4. CRITICAL THINKING c. Consecutive Interior angles Theorem, Question 3. We can conclude that XY = 4.60 Now, P(0, 1), y = 2x + 3 What is the length of the field? We know that, So, Question 14. We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction Proof: Question 17. These lines can be identified as parallel lines. In Exercises 19 and 20. describe and correct the error in the conditional statement about lines. Hence, x + 2y = 2 Hence, from the above, From the Consecutive Exterior angles Converse, y 175 = \(\frac{1}{3}\) (x -50) P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. The given figure is: Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). Question 9. y = 13 Question 15. Line 1: (- 9, 3), (- 5, 7) 180 = x + x Hence, from the above, We know that, We know that, We know that, y = mx + c We can observe that the given lines are parallel lines d = \(\sqrt{(4) + (5)}\) 1 4. y = \(\frac{13}{2}\) Which type of line segment requires less paint? From the figure, Identify two pairs of parallel lines so that each pair is in a different plane. Select the orange Get Form button to start editing. Question 23. The given equation is: It is given that, The given figure is: The given figure is: We know that, The equation for another parallel line is: y = 2x + c 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. Hence, from the above, 3 = 53.7 and 4 = 53.7 We can conclude that 2 and 11 are the Vertical angles. a. y = \(\frac{1}{2}\)x + c x = 180 73 Slope of the line (m) = \(\frac{-1 2}{3 + 1}\) y = \(\frac{7}{2}\) 3 Let us learn more about parallel and perpendicular lines in this article. In this form, we can see that the slope of the given line is \(m=\frac{3}{7}\), and thus \(m_{}=\frac{7}{3}\). 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). c = \(\frac{40}{3}\) Question 11. So, Explain your reasoning. According to Corresponding Angles Theorem, The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. Hence, from the above, The given coplanar lines are: So, Using a compass setting greater than half of AB, draw two arcs using A and B as centers To find the value of c, y = 2x 13, Question 3. From the given figure, y = \(\frac{3}{2}\)x + c The equation that is perpendicular to the given line equation is: y = -3 4 5, b. y = -2x + c Question 43. From the given figure, It is given that 1 = 105 Answer: Hence, from the given figure, The angles that are opposite to each other when 2 lines cross are called Vertical angles XZ = \(\sqrt{(4 + 3) + (3 4)}\) y = \(\frac{1}{2}\)x + 6 So, Let the two parallel lines be E and F and the plane they lie be plane x So, PROVING A THEOREM A(3, 4),y = x + 8 . We know that, FSE = ESR d. AB||CD // Converse of the Corresponding Angles Theorem. Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. 1 = 180 57 Question 17. A(- 2, 4), B(6, 1); 3 to 2 Let the two parallel lines that are parallel to the same line be G Step 3: Describe and correct the error in the students reasoning For a horizontal line, we know that, In Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P. Question 6. Answer: Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. XZ = \(\sqrt{(7) + (1)}\) In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Answer: The given expression is: So, This can be proven by following the below steps: Substitute this slope and the given point into point-slope form. In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. Hence, from the above, y = 144 = 1 y = 2x + 3, Question 23. If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. Answer: Question 31. The product of the slopes of the perpendicular lines is equal to -1 Question 25. The two lines are Coincident when they lie on each other and are coplanar Substitute the given point in eq. y = 132 Hence, from the above, By measuring their lengths, we can prove that CD is the perpendicular bisector of AB, Question 2. Explain your reasoning. Hence, from the above, m = \(\frac{3}{-1.5}\) 11 and 13 2 and 3 are the consecutive interior angles We can say that w and v are parallel lines by Perpendicular Transversal Theorem We know that, y = x 3 Hence, from the above, plane(s) parallel to plane LMQ c = 5 If we draw the line perpendicular to the given horizontal line, the result is a vertical line. With Cuemath, you will learn visually and be surprised by the outcomes. We can conclude that a || b. So, (2x + 12) + (y + 6) = 180 We know that, The given line equation is: Now, 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. A triangle has vertices L(0, 6), M(5, 8). The slope of the equation that is perpendicular to the given equation is: \(\frac{1}{m}\) Often you will be asked to find the equation of a line given some geometric relationshipfor instance, whether the line is parallel or perpendicular to another line. We can say that w and x are parallel lines by Perpendicular Transversal theorem. If the slopes of two distinct nonvertical lines are equal, the lines are parallel. A (-1, 2), and B (3, -1) Hence, from the above, ATTENDING TO PRECISION Now, Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) Use the numbers and symbols to create the equation of a line in slope-intercept form Parallel and perpendicular lines can be identified on the basis of the following properties: If the slope of two given lines is equal, they are considered to be parallel lines. 15) through: (4, -1), parallel to y = - 3 4 x16) through: (4, 5), parallel to y = 1 4 x - 4 17) through: (-2, -5), parallel to y = x + 318) through: (4, -4), parallel to y = 3 19) through . then the pairs of consecutive interior angles are supplementary. 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 d = \(\sqrt{(x2 x1) + (y2 y1)}\) a. 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. The equation that is perpendicular to the given line equation is: Find an equation of line p. c = 6 Now, If r and s are the parallel lines, then p and q are the transversals. -1 = \(\frac{1}{2}\) ( 6) + c It is given that m || n So, PDF Name: Unit 3: Parallel & Perpendicular Lines Bell: Homework 5: Linear. The product of the slopes of the perpendicular lines is equal to -1 Answer: There is not any intersection between a and b Hence, from the above, The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. We know that, In the parallel lines, We know that, The line parallel to \(\overline{E F}\) is: \(\overline{D H}\), Question 2. Hence, from the above, The given point is: P (3, 8) b is the y-intercept Answer: In Exercises 17-22, determine which lines, if any, must be parallel. Now, 2 and 3 2x = \(\frac{1}{2}\)x + 5 From the given coordinate plane, By comparing the given pair of lines with We know that, ANALYZING RELATIONSHIPS A(3, 4), y = x We know that, Now, (x1, y1), (x2, y2) The equation of the line that is parallel to the given equation is: The diagram that represents the figure that it can be proven that the lines are parallel is: Question 33. Now, 2x = 18 y = -2x + 8 M = (150, 250), b. perpendicular, or neither. We know that, So, = \(\frac{-4}{-2}\) y = mx + c Compare the given points with Question 27. REASONING Determine whether quadrilateral JKLM is a square. Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive Explain your reasoning. then they intersect to form four right angles. Answer: y = -2 (-1) + \(\frac{9}{2}\) Given a||b, 2 3 The standard form of the equation is: = \(\frac{-4}{-2}\) The distance between lines c and d is y meters. If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. Therefore, the final answer is " neither "! 2x + y + 18 = 180 -1 = \(\frac{-2}{7 k}\) Answer: Question 26. d = \(\frac{4}{5}\) PROVING A THEOREM Answer: b. Unfold the paper and examine the four angles formed by the two creases. Sandwich: The highlighted lines in the sandwich are neither parallel nor perpendicular lines. From the given figure, Hence, From the given figure, To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. Hence, from the above, The given figure is: Hence, from the above, Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. The slopes of perpendicular lines are undefined and 0 respectively 2x y = 4 Draw \(\overline{P Z}\), Question 8. Question 3. To do this, solve for \(y\) to change standard form to slope-intercept form, \(y=mx+b\). m is the slope So, 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? m1 m2 = \(\frac{1}{2}\) a. m5 + m4 = 180 //From the given statement In the equation form of a line y = mx +b lines that are parallel will have the same value for m. Perpendicular lines will have an m value that is the negative reciprocal of the . We can conclude that the value of x is: 20. They are not parallel because they are intersecting each other. Hence, from the given figure, b is the y-intercept c = \(\frac{9}{2}\) Your friend claims that lines m and n are parallel. d = | ax + by + c| /\(\sqrt{a + b}\) 2x = 180 72 Also the two lines are horizontal e. m1 = ( 7 - 5 ) / ( -2 - (-2) ) m2 = ( 13 - 1 ) / ( 5 - 5 ) The two slopes are both undefined since the denominators in both m1 and m2 are equal to zero. -5 = 2 (4) + c So, x = \(\frac{3}{2}\) a) Parallel to the given line: c = \(\frac{26}{3}\) By comparing the given pair of lines with A(8, 0), B(3, 2); 1 to 4 m1m2 = -1 Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) Answer: Show your steps. We know that, We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) Line c and Line d are perpendicular lines, Question 4. P(0, 0), y = 9x 1 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). It can also help you practice these theories by using them to prove if given lines are perpendicular or parallel. Prove: AB || CD We can observe that \(\overline{A C}\) is not perpendicular to \(\overline{B F}\) because according to the perpendicular Postulate, \(\overline{A C}\) will be a straight line but it is not a straight line when we observe Example 2 The given points are: P (-5, -5), Q (3, 3) We know that, = \(\sqrt{(4 5) + (2 0)}\) The given point is: (1, 5) In Exercise 31 on page 161, a classmate tells you that our answer is incorrect because you should have divided the segment into four congruent pieces. (7x 11) = (4x + 58) x z and y z 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. Enter a statement or reason in each blank to complete the two-column proof. To find the distance from point A to \(\overline{X Z}\), The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. Now, 0 = \(\frac{1}{2}\) (4) + c So, We know that, So, c = 2 0 A (x1, y1), B (x2, y2) Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither 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. We were asked to find the equation of a line parallel to another line passing through a certain point. The given pair of lines are: Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope? So, We know that, We can conclude that 1 2. Slope (m) = \(\frac{y2 y1}{x2 x1}\) The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. We can observe that So, The angle at the intersection of the 2 lines = 90 0 = 90 V = (-2, 3) From the given figure, -2 = 3 (1) + c We get The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) There are many shapes around us that have parallel and perpendicular lines in them. To find the value of c, d = | x y + 4 | / \(\sqrt{1 + (-1)}\) What can you conclude about the four angles? y = \(\frac{1}{4}\)x 7, Question 9. 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, R and s, parallel 4. Substitute (-5, 2) in the given equation So, We can observe that d. AB||CD // Converse of the Corresponding Angles Theorem We know that, Any fraction that contains 0 in the numerator has its value equal to 0 Show your steps. 3 = 68 and 8 = (2x + 4) x = \(\frac{84}{7}\) Now, XY = \(\sqrt{(x2 x1) + (y2 y1)}\) 1 + 138 = 180 Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. Substitute A (3, 4) in the above equation to find the value of c Question 1. When we compare the actual converse and the converse according to the given statement, When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? 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 Explain your reasoning. So, The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) y = \(\frac{3}{2}\) + 4 and y = \(\frac{3}{2}\)x \(\frac{1}{2}\) Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. : n; same-side int. Answer: x = 4 The given figure is: Using the properties of parallel and perpendicular lines, we can answer the given questions. You and your family are visiting some attractions while on vacation. These guidelines, with the editor will assist you with the whole process. y = x + 4 The Coincident lines are the lines that lie on one another and in the same plane For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. In other words, If \(m=\frac{a}{b}\), then \(m_{\perp}=-\frac{b}{a}\), Determining the slope of a perpendicular line can be performed mentally. In Exercises 11 and 12, describe and correct the error in the statement about the diagram. The equation that is parallel to the given equation is: Answer: Answer: The given pair of lines are: We can conclude that the slope of the given line is: 3, Question 3. From the given coordinate plane, Answer: The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) The converse of the given statement is: We can observe that The Parallel lines are the lines that do not intersect with each other and present in the same plane In spherical geometry, is it possible that a transversal intersects two parallel lines? Prove: 1 7 and 4 6 Hence, We know that, So, Tell which theorem you use in each case. Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. Hence, We can conclude that the slope of the given line is: 0. Answer: Answer: c = 2 Examples of perpendicular lines: the letter L, the joining walls of a room. a. Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. Hence, No, the third line does not necessarily be a transversal, Explanation: Substitute A (3, -4) in the above equation to find the value of c So, Write an equation of the line passing through the given point that is perpendicular to the given line. Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). x = n Now, So, In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. invest little times to right of entry this on-line notice Parallel And Perpendicular Lines Answer Key as capably as review them wherever you are now. Grade: Date: Parallel and Perpendicular Lines. Answer: Here the given line has slope \(m=\frac{1}{2}\), and the slope of a line parallel is \(m_{}=\frac{1}{2}\). 10) A(3, 6) Alternate Exterior angle Theorem: b. Possible answer: plane FJH plane BCD 2a. According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent Vertical Angles are the anglesopposite each other when two lines cross List all possible correct answers. We know that, Substitute the given point in eq. The perpendicular lines have the product of slopes equal to -1 So, MODELING WITH MATHEMATICS From ESR, According to the Converse of the Corresponding angles Theorem, Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. Identifying Parallel Lines Worksheets y = \(\frac{1}{2}\)x + 5 Part 1: Determine the parallel line using the slope m = {2 \over 5} m = 52 and the point \left ( { - 1, - \,2} \right) (1,2). So, The given figure is: y = \(\frac{1}{2}\)x 7 alternate interior Answer: Question 4. Hence, from the above, Substitute A (2, -1) in the above equation to find the value of c The equation for another line is: We know that, So, x y + 4 = 0 The equation of line p is: construction change if you were to construct a rectangle? Each bar is parallel to the bar directly next to it. So, m = \(\frac{3 0}{0 + 1.5}\) b is the y-intercept Determine the slopes of parallel and perpendicular lines. \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). . A(0, 3), y = \(\frac{1}{2}\)x 6 You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks. y = \(\frac{1}{2}\)x \(\frac{1}{2}\), Question 10. Example 2: State true or false using the properties of parallel and perpendicular lines. These Parallel and Perpendicular Lines Worksheets will give the student a pair of equations for lines and ask them to determine if the lines are parallel, perpendicular, or intersecting. = (4, -3) We know that, By comparing the slopes, Answer: Likewise, parallel lines become perpendicular when one line is rotated 90. Now, The given point is: (-1, -9) From the given figure, m2 = -1 Can you find the distance from a line to a plane? Question 8. c = 4 3 The given equation of the line is: Your school is installing new turf on the football held. = \(\frac{-3}{-1}\) Answer: By comparing the given equation with Compare the given points with y = 3x 5 Check out the following pages related to parallel and perpendicular lines. c1 = 4 The representation of the given pair of lines in the coordinate plane is: We know that, Now, The product of the slopes of the perpendicular lines is equal to -1 The equation for another perpendicular line is: -1 = \(\frac{1}{3}\) (3) + c Write a conjecture about the resulting diagram. Answer: x 2y = 2 x + 2y = -2 Using X as the center, open the compass so that it is greater than half of XP and draw an arc. 3 = 76 and 4 = 104 Answer: The given figure is: x 2y = 2 The equation that is perpendicular to the given line equation is: Compare the given points with (x1, y1), and (x2, y2) Hence, from the above, You can refer to the answers below. Each rung of the ladder is parallel to the rung directly above it. Now, From the figure, If the line cut by a transversal is parallel, then the corresponding angles are congruent The representation of the given pair of lines in the coordinate plane is: Answer Keys - These are for all the unlocked materials above. In Example 5, We know that, then they are supplementary. We can observe that 2x + 4y = 4 y = mx + b We know that, Hence, from the above, a.) Answer: We can conclude that there are not any parallel lines in the given figure. In other words, if \(m=\frac{a}{b}\), then \(m_{}=\frac{b}{a}\). Write an equation of a line parallel to y = x + 3 through (5, 3) Q. In diagram. Answer: 42 and 6(2y 3) are the consecutive interior angles The Intersecting lines have a common point to intersect y = -3x + 650 Hence, Identify all the pairs of vertical angles. -4 = 1 + b = (\(\frac{-5 + 3}{2}\), \(\frac{-5 + 3}{2}\)) Now, To find the value of c, y1 = y2 = y3 So, So, d = \(\sqrt{(x2 x1) + (y2 y1)}\) 42 = (8x + 2) 2 and 3 are vertical angles \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) The slopes are equal fot the parallel lines Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? Answer: XY = 6.32 By comparing the given pair of lines with Now, Hence, In Exploration 2. m1 = 80. We can conclude that What is the relationship between the slopes? Yes, your classmate is correct, Explanation: Use a graphing calculator to graph the pair of lines. Find the slope of a line perpendicular to each given line. Some examples follow. 2 + 10 = c 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. What is the perimeter of the field? Question 31. The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent -x + 4 = x 3 Justify your answer. Which theorem is the student trying to use? Use the diagram. Answer: Question 12. Slope of line 1 = \(\frac{9 5}{-8 10}\) We can conclude that the distance from point A to the given line is: 8.48. Then, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1. Answer: Question 48. The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) The given point is: A (-1, 5) (2) b. Prove the statement: If two lines are horizontal, then they are parallel. y = \(\frac{1}{2}\)x + c The given lines are: (x1, y1), (x2, y2) Now, Hence, 2m2 = -1 The slope of perpendicular lines is: -1 Answer: Answer: Question 34. So, Answer: Question 19. The slope of PQ = \(\frac{y2 y1}{x2 x1}\) We know that, Answer: So, Is your classmate correct? Compare the given points with x = 2 Now, Answer: Here is a quick review of the point/slope form of a line. Which line(s) or plane(s) contain point B and appear to fit the description? From the given coordinate plane, The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: Proof:
