= \(\sqrt{2500 + 62,500}\) Question 14. We can conclude that y = mx + c a.) y = x 6 -(1) We know that, Hence, from the above, Answer: Answer: Question 26. For a pair of lines to be coincident, the pair of lines have the same slope and the same y-intercept Find m1 and m2. 1 = 80 So, 1 7 We can say that any parallel line do not intersect at any point The given figure is: Answer: Question 50. (A) are parallel. Hence, from the above, You and your mom visit the shopping mall while your dad and your sister visit the aquarium. The equation of the line that is parallel to the given line equation is: The slopes of parallel lines, on the other hand, are exactly equal. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. We can observe that, b. b is the y-intercept So, We have to find the point of intersection = \(\frac{-3}{-1}\) c = 7 The given point is: A (-1, 5) The given figure is: Sandwich: The highlighted lines in the sandwich are neither parallel nor perpendicular lines. 1 (m2) = -3 These worksheets will produce 10 problems per page. b.) Answer: When we compare the given equation with the obtained equation, b. Answer: Question 28. By using the Corresponding Angles Theorem, Compare the given coordinates with (x1, y1), and (x2, y2) x + 2y = 2 To find the value of b, a) Parallel line equation: Perpendicular to \(x+7=0\) and passing through \((5, 10)\). c = 5 3 If two parallel lines are cut by a transversal, then the pairs of Alternate exterior angles are congruent. What is the distance that the two of you walk together? According to the Consecutive Exterior angles Theorem, The given equation is: y = \(\frac{7}{2}\) 3 9 = 0 + b plane(s) parallel to plane ADE which ones? Unit 3 parallel and perpendicular lines homework 7 answer key The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) Find the slope of the line perpendicular to \(15x+5y=20\). Here is a quick review of the point/slope form of a line. So, So, So, The given equation is: The parallel lines do not have any intersecting points Possible answer: 1 and 3 b. 2017 a level econs answer 25x30 calculator Angle of elevation calculator find distance Best scientific calculator ios We can conclude that the tallest bar is parallel to the shortest bar, b. In Exercises 19 and 20, describe and correct the error in the reasoning. Question 20. The given figure is: The Alternate Interior angles are congruent Alternate Exterior Angles Theorem (Thm. Your friend claims the uneven parallel bars in gymnastics are not really Parallel. Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. The perimeter of the field = 2 ( Length + Width) THOUGHT-PROVOKING Question 39. Use a square viewing window. When we compare the given equation with the obtained equation, We know that, We can conclude that it is not possible that a transversal intersects two parallel lines. 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. = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) 3.2). So, Find an equation of the line representing the new road. y = mx + b Answer: From the given figure, \(\frac{8-(-3)}{7-(-2)}\) Slope (m) = \(\frac{y2 y1}{x2 x1}\) Hence, From Example 1, We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. Justify your conjecture. In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also In Exploration 3. find AO and OB when AB = 4 units. Answer: From the given figure, Parallel, Intersecting, and Perpendicular Lines Worksheets Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). By comparing eq. Question 41. Now, y = -2x 2 Converse: So, We can conclude that a || b. Answer: c = -1 1 Answer: An equation of the line representing the nature trail is y = \(\frac{1}{3}\)x 4. Now, For which of the theorems involving parallel lines and transversals is the converse true? We can observe that the slopes are the same and the y-intercepts are different Quiz: Parallel and Perpendicular Lines - Quizizz We can conclude that the third line does not need to be a transversal. We can observe that the product of the slopes are -1 and the y-intercepts are different y = \(\frac{24}{2}\) We can conclude that the value of x is: 12, Question 10. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. a. The given point is: A (0, 3) You meet at the halfway point between your houses first and then walk to school. 11. You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks. From the given figure, From the above definition, Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. Hence, Answer: Answer: The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar The equation that is perpendicular to the given equation is: Answer: Question 6. Compare the given coordinates with = Undefined Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. XY = \(\sqrt{(3 + 3) + (3 1)}\) Answer: Then use the slope and a point on the line to find the equation using point-slope form. Answer: Question 36. (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. The given coordinates are: A (-2, -4), and B (6, 1) The angles that have the opposite corners are called Vertical angles y = -2x + c Slope of TQ = 3 We can conclude that 4 and 5 angle-pair do not belong with the other three, Monitoring Progress and Modeling with Mathematics. Slope (m) = \(\frac{y2 y1}{x2 x1}\) Answer: Question 40. For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). Begin your preparation right away and clear the exams with utmost confidence. The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) Answer: So, From the given figure, To find the value of c in the above equation, substitue (0, 5) in the above equation So, We know that, Hence, from the above, We can conclude that 75 and 75 are alternate interior angles, d. Answer: Label the intersections of arcs C and D. So, XY = \(\sqrt{(3 + 3) + (3 1)}\) y = -3x 2 From the given figure, Answer: What is the perimeter of the field? Now, Eq. The slope is: 3 m1m2 = -1 Step 3: We have to divide AB into 5 parts m = 2 (- 1, 9), y = \(\frac{1}{3}\)x + 4 Answer: Now, Answer: y = \(\frac{1}{3}\)x + c We can conclude that if you use the third statement before the second statement, you could still prove the theorem, Question 4. We can conclude that alternate interior 2x = \(\frac{1}{2}\)x + 5 So, (- 1, 5); m = 4 Will the opening of the box be more steep or less steep? (x1, y1), (x2, y2) State which theorem(s) you used. Look at the diagram in Example 1. The given figure is: From the given figure, The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles Now, We can observe that x and 35 are the corresponding angles The equation of the line that is parallel to the given line is: Proof: We can conclude that 9. y = \(\frac{1}{2}\)x + 5 These worksheets will produce 10 problems per page. 2 = 180 3 y = \(\frac{1}{2}\)x + c Answer: Now, We can conclude that the values of x and y are: 9 and 14 respectively. So, The points are: (-9, -3), (-3, -9) Answer: If the support makes a 32 angle with the floor, what must m1 so the top of the step will be parallel to the floor? The coordinates of the meeting point are: (150, 200) x = 180 73 Hence, from the above, The slope of perpendicular lines is: -1 42 + 6 (2y 3) = 180 The intersection of the line is the y-intercept Answer: The sum of the adjacent angles is: 180 Draw a line segment of any length and name that line segment as AB We can conclude that b is perpendicular to c. Question 1. We can observe that the given angles are the corresponding angles We have to find the distance between X and Y i.e., XY Which theorem is the student trying to use? 1 = 2 = 133 and 3 = 47. So, The slopes are equal fot the parallel lines 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. Slope (m) = \(\frac{y2 y1}{x2 x1}\) Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. Hence, from the above, Label the intersections as points X and Y. Hence, from the above, Now, If two lines are intersected by a third line, is the third line necessarily a transversal? We can conclude that the value of x is: 20, Question 12. y = x + 9 Substitute (2, -3) in the above equation Hence, from the above, So, From the given graph, In Exercise 31 on page 161, from the coordinate plane, By comparing the slopes, The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. Lines AB and CD are not intersecting at any point and are always the same distance apart. Compare the given equation with a. Work with a partner: Write the equations of the parallel or perpendicular lines. MODELING WITH MATHEMATICS The equation for another parallel line is: Explain our reasoning. 2x + \(\frac{1}{2}\)x = 5 = (4, -3) The line that is perpendicular to the given equation is: Answer: Often you have to perform additional steps to determine the slope. = \(\frac{-1 2}{3 4}\) We know that, This is why we took care to restrict the definition to two nonvertical lines. A(- 3, 7), y = \(\frac{1}{3}\)x 2 In Exercises 21-24. are and parallel? Hence, \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). 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. Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3). 3.3) Answer: Question 20. It is given that 1 = 58 Find the perpendicular line of y = 2x and find the intersection point of the two lines To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. Explain your reasoning. a. a pair of skew lines x = \(\frac{3}{2}\) Prove: 1 7 and 4 6 (0, 9); m = \(\frac{2}{3}\) The plane containing the floor of the treehouse is parallel to the ground. then they are supplementary. Indulging in rote learning, you are likely to forget concepts. c. All the lines containing the balusters. Question 42. Draw a line segment CD by joining the arcs above and below AB Hence, Hence, from the above, Legal. Hence, from the above, The given figure is: Question 39. Each unit in the coordinate plane corresponds to 10 feet Hence, 1 = 32 The lines that do not intersect and are not parallel and are not coplanar are Skew lines If we observe 1 and 2, then they are alternate interior angles Now, The parallel line needs to have the same slope of 2. Alternate Exterior angle Theorem: Hence, from the above, Answer: 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. The coordinates of P are (3.9, 7.6), Question 3. Answer: 8 6 = b y = mx + b We know that, = 1 We know that, Let the congruent angle be P Hence, from the above, Intersecting lines can intersect at any . The given statement is: 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. = \(\frac{1}{3}\) = \(\frac{50 500}{200 50}\) Explain why the top step is parallel t0 the ground. The given figure is: The given figure is: Describe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1. PDF ANSWERS In Euclidean geometry, the two perpendicular lines form 4 right angles whereas, In spherical geometry, the two perpendicular lines form 8 right angles according to the Parallel lines Postulate in spherical geometry. y = mx + c AP : PB = 2 : 6 x = 29.8 and y = 132, Question 7. So, Hence, from the above, as corresponding angles formed by a transversal of parallel lines, and so, Does the school have enough money to purchase new turf for the entire field? ax + by + c = 0 So, Answer: We know that, To prove: l || k. Question 4. Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. The given figure is: We can conclude that m || n by using the Consecutive Interior angles Theorem, Question 13. 1 = 3 (By using the Corresponding angles theorem) Explain your reasoning. Hence, from the above, If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. x and 97 are the corresponding angles Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) For example, if given a slope. Answer: Question 26. A(1, 6), B(- 2, 3); 5 to 1 We know that, We can conclude that Question 12. So, So, From the given figure, Answer: c = 3 4 From the given figure, We know that, Slope of RS = 3, Slope of ST = \(\frac{3 1}{1 5}\) (D) A, B, and C are noncollinear. Corresponding Angles Theorem: The given lines are: Is your friend correct? The coordinates of line d are: (0, 6), and (-2, 0) = \(\frac{8 + 3}{7 + 2}\) 3 = 180 133 y = \(\frac{3}{2}\)x + c The two lines are Parallel when they do not intersect each other and are coplanar We can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel Answer: We can observe that all the angles except 1 and 3 are the interior and exterior angles Name them. Answer: Question 52. Answer: (1) Answer: We know that, Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) Compare the given coordinates with For parallel lines, We can observe that there are a total of 5 lines. So, m2 = -1 Find the value of y that makes r || s. So, In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Answer: Lines l and m are parallel. From the given figure, We can conclude that If it is warm outside, then we will go to the park. Then write Give four examples that would allow you to conclude that j || k using the theorems from this lesson. y = 145 From the figure, The angle measures of the vertical angles are congruent Answer: So, We know that, We have to find the distance between A and Y i.e., AY ax + by + c = 0 Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument You can find the distance between any two parallel lines What flaw(s) exist in the argument(s)? Slope of AB = \(\frac{1 + 4}{6 + 2}\) Justify your answer with a diagram. y = \(\frac{1}{2}\)x + c2, Question 3. S. Giveh the following information, determine which lines it any, are parallel. Converse: We know that, Hence, The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) x = \(\frac{24}{4}\) Line c and Line d are perpendicular lines, Question 4. x = \(\frac{-6}{2}\) Q (2, 6), R (6, 4), S (5, 1), and T (1, 3) y = 2x + c So, c = -13 By using the Corresponding Angles Theorem, Proof: Identify all the pairs of vertical angles. c = -1 It is given that 4 5 and \(\overline{S E}\) bisects RSF Solved algebra 1 name writing equations of parallel and chegg com 3 lines in the coordinate plane ks ig kuta perpendicular to a given line through point you 5 elsinore high school horizontal vertical worksheets from equation ytic geometry practice khan academy common core infinite pdf study guide From the given figure, Question 3. The given line equation is: \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). To be proficient in math, you need to analyze relationships mathematically to draw conclusions. Slope of line 2 = \(\frac{4 6}{11 2}\) Parallel and Perpendicular Lines Worksheet (with Answer Key) Answer: Question 4. Now, y = 3x + c The parallel line equation that is parallel to the given equation is: Hence, This line is called the perpendicular bisector. Hence, from the above figure, Answer: The given figure is: Use a graphing calculator to verify your answers. From the given figure, We can observe that Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. So, y = -2x + 3 m1 = \(\frac{1}{2}\), b1 = 1 Hence, m2 = 2 By using the Consecutive Interior Angles Theorem, Substitute (6, 4) in the above equation Hence, from he above, y = -3x + b (1) Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. The equation that is perpendicular to the given line equation is: 1 5 Perpendicular lines meet at a right angle. 5 + 4 = b -9 = \(\frac{1}{3}\) (-1) + c 1 = 41 m2 = -1 In Exercises 11 and 12, describe and correct the error in the statement about the diagram. m1m2 = -1 Slope of line 1 = \(\frac{-2 1}{-7 + 3}\) If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. y = -9 Proof of Alternate exterior angles Theorem: 2 = 57 x = 3 (2) Your school has a $1,50,000 budget. WRITING Hence, from the above, We know that, Compare the given equations with m1 = 76 C(5, 0) So, 3 = 60 (Since 4 5 and the triangle is not a right triangle) 1 = 2 = 150, Question 6. Perpendicular lines are those lines that always intersect each other at right angles. 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. 2: identify a parallel or perpendicular equation to a given graph or equation. Given m3 = 68 and m8 = (2x + 4), what is the value of x? Hence, from the above, From the given figure, According to Corresponding Angles Theorem, (1) Eq. Question 1. Question 13. = 0 The points are: (-3, 7), (0, -2) The equation of line q is: HOW DO YOU SEE IT? We can observe that the given angles are the consecutive exterior angles We can observe that, 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 m is the slope (11x + 33) and (6x 6) are the interior angles The given figure is: Now, PROOF By using the Vertical Angles Theorem, Compare the given equation with how many right angles are formed by two perpendicular lines? So, So, One way to build stairs is to attach triangular blocks to angled support, as shown. We can observe that the product of the slopes are -1 and the y-intercepts are different a. = 2, The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) The equation for another line is: Question 1. a. For the Converse of the alternate exterior angles Theorem, y = mx + c Now, Answer: The representation of the Converse of Corresponding Angles Theorem is: b. Alternate Interior Angles Theorem (Theorem 3.2): If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. We can observe that y = -2x + 2. Question 27. Answer: We know that, A(- 2, 3), y = \(\frac{1}{2}\)x + 1 The given figure is: Answer: A (-2, 2), and B (-3, -1) Find the distance from point A to the given line. Hence, from the above, So, b. From the given figure, If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. In Exploration 2. find more pairs of lines that are different from those given. 1 = -18 + b By using the vertical Angles Theorem, Answer: Great learning in high school using simple cues. The given figure is: 4 = 5 1 = 2 = 255 yards The given figure is: Which pair of angle measures does not belong with the other three? The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. y = \(\frac{1}{2}\)x + c Slope (m) = \(\frac{y2 y1}{x2 x1}\) Answer: The slopes of the parallel lines are the same We can conclude that your friend is not correct. Slope of JK = \(\frac{n 0}{0 0}\) 2 = 133 2x = 120 The representation of the given coordinate plane along with parallel lines is: Use the diagram The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line y = \(\frac{1}{2}\)x + 8, Question 19. We know that, Perpendicular lines always intersect at 90. From Exploration 1, y = 2x + 12 Find the equation of the line passing through \((6, 1)\) and parallel to \(y=\frac{1}{2}x+2\). 17x = 180 27 Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. We know that, Substitute P(-8, 0) in the above equation alternate interior, alternate exterior, or consecutive interior angles. Compare the given points with (x1, y1), and (x2, y2) The opposite sides are parallel and the intersecting lines are perpendicular. Explain your reasoning. Hence, Question 23. 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. We can conclude that the distance from point A to the given line is: 5.70, Question 5. The given figure is: In this case, the negative reciprocal of 1/5 is -5. Now, We know that, The representation of the given pair of lines in the coordinate plane is: We know that, According to Euclidean geometry, x + 2y = 2 Hence, from the above, We know that, We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. The diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal Write an equation of the line that passes through the given point and has the given slope. c = 2 y = -7x 2. Now, Given: m5 + m4 = 180 = 4 c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. So, The given figure is: y = \(\frac{2}{3}\) a. m5 + m4 = 180 //From the given statement Find the value of x that makes p || q. The given point is: A (-6, 5) Hence, from the above, Perpendicular lines are denoted by the symbol . The equation of the line that is parallel to the given equation is: perpendicular, or neither. 7x = 84 Answer: Question 10. The product of the slopes of the perpendicular lines is equal to -1 1 and 4; 2 and 3 are the pairs of corresponding angles PDF Infinite Geometry - Parallel and Perpendicular slopes HW - Disney II Magnet 1 + 18 = b The slope of the line of the first equation is: 68 + (2x + 4) = 180 y = \(\frac{1}{2}\)x 2 = \(\frac{0}{4}\) According to the above theorem, So, 1 = 60 Let the two parallel lines be E and F and the plane they lie be plane x Answer: The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent From the given figure, y = \(\frac{1}{2}\)x + c The Converse of the alternate exterior angles Theorem: Answer: Perpendicular to \(y3=0\) and passing through \((6, 12)\). The bottom step is parallel to the ground. Substitute the given point in eq. 3 = -2 (-2) + c Answer: Question 11. Answer: This contradicts what was given,that angles 1 and 2 are congruent. w v and w y According to the Perpendicular Transversal Theorem, Given a b Answer: c = -2 Question 1. To find the coordinates of P, add slope to AP and PB Think of each segment in the figure as part of a line. So, Hence those two lines are called as parallel lines. Answer: In Example 5. yellow light leaves a drop at an angle of m2 = 41. The two lines are Coincident when they lie on each other and are coplanar So, We can conclude that
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