In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. We know that, We have to divide AB into 5 parts Answer: Question 36. Identifying Parallel Lines Worksheets Answer: Is it possible for consecutive interior angles to be congruent? From the given figure, Explain why the top rung is parallel to the bottom rung. = \(\frac{3}{4}\) If the pairs of corresponding angles are, congruent, then the two parallel lines are. The alternate interior angles are: 3 and 5; 2 and 8, c. alternate exterior angles w v and w y y = \(\frac{1}{3}\)x + \(\frac{475}{3}\), c. What are the coordinates of the meeting point? In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. Answer: justify your answer. Use the numbers and symbols to create the equation of a line in slope-intercept form From the given figure, Tell which theorem you use in each case. We know that, So, 1 = 180 138 The representation of the given coordinate plane along with parallel lines is: Substitute A (6, -1) in the above equation which ones? m1 m2 = -1 x = \(\frac{69}{3}\) m = = So, slope of the given line is Question 2. A(3, 4),y = x + 8 Now, Question 3. (1) b.) a. The equation of a line is: 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. The slope of the given line is: m = 4 Answer: Question 2. y = mx + b The perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle. Hence, 6x = 87 The given equation is: Here 'a' represents the slope of the line. From the given figure, Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Answer: In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning. plane(s) parallel to plane ADE So, y = -2 (5y 21) = (6x + 32) (b) perpendicular to the given line. 3.6: Parallel and Perpendicular Lines - Mathematics LibreTexts Proof: Now, The Alternate Interior angles are congruent c = -5 We can conclude that From the given figure, Answer Keys - These are for all the unlocked materials above. So, The distance from your house to the school is one-fourth of the distance from the school to the movie theater. 8 = 180 115 ID Unit 3: Paraliel& Perpendicular Lines Homework 3: | Chegg.com x = \(\frac{24}{4}\) The equation that is parallel to the given equation is: The third intersecting line can intersect at the same point that the two lines have intersected as shown below: 1 = 123 The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: We can conclude that m || n, Question 15. Answer: So, The given equation is: m2 = \(\frac{1}{3}\) We can conclude that Substitute A (-6, 5) in the above equation to find the value of c -5 = 2 (4) + c A Linear pair is a pair of adjacent angles formed when two lines intersect The given point is: A (3, -4) = | 4 + \(\frac{1}{2}\) | By comparing eq. From the given figure, 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. We can conclude that the value of x is: 60, Question 6. = 180 76 Using the properties of parallel and perpendicular lines, we can answer the given questions. y = 4x + 9, Question 7. We can conclude that it is not possible that a transversal intersects two parallel lines. The given figure is: a = 2, and b = 1 d. AB||CD // Converse of the Corresponding Angles Theorem. According to Contradiction, Possible answer: 1 and 3 b. -3 = -2 (2) + c XY = 6.32 Answer: The equation for another parallel line is: Question 5. The given equation is: If we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0 Perpendicular lines are those lines that always intersect each other at right angles. 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? Now, So, We know that, Parallel & Perpendicular Lines: Answer Key (x1, y1), (x2, y2) Draw an arc with center A on each side of AB. y = \(\frac{1}{2}\)x + 1 -(1) The slopes of the parallel lines are the same x + 2y = 10 A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. So, Proof: m2 = \(\frac{1}{2}\) So, We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. The perpendicular lines have the product of slopes equal to -1 \(m_{}=\frac{3}{2}\) and \(m_{}=\frac{2}{3}\), 19. We know that, 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 Substitute (4, -5) in the above equation 2 = 133 y = \(\frac{13}{2}\) What point on the graph represents your school? The given figure is: Answer: The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. So, y = 2x + c2, b. (1) with the y = mx + c, From the given figure, The parallel lines have the same slope The distance between the perpendicular points is the shortest Answer: Question 46. The slopes are equal fot the parallel lines (x1, y1), (x2, y2) y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) The given equation is: Justify your answer. Now, Solution: We need to know the properties of parallel and perpendicular lines to identify them. We can observe that 2 and 3 So, Parallel, Intersecting, and Perpendicular Lines Worksheets So, Write the converse of the conditional statement. Prove 1, 2, 3, and 4 are right angles. Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3). Consecutive Interior Angles Converse (Theorem 3.8) The product of the slopes of the perpendicular lines is equal to -1 Question 13. Justify your answer with a diagram. The given figure is: Substitute (1, -2) in the above equation Answer: Two lines are cut by a transversal. For the proofs of the theorems that you found to be true, refer to Exploration 1. The coordinates of P are (3.9, 7.6), Question 3. Show your steps. 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. Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent 2x = 135 15 Compare the given points with (x1, y1), and (x2, y2) Slope of KL = \(\frac{n n}{n 0}\) DOC Geometry - Loudoun County Public Schools We can conclude that m || n by using the Consecutive Interior angles Theorem, Question 13. To find the value of c, Hence, from the above, We can say that all the angle measures are equal in Exploration 1 2m2 = -1 The representation of the given point in the coordinate plane is: Question 54. So, The equation that is parallel to the given equation is: Compare the given points with (x1, y1), and (x2, y2) Compare the given points with We know that, Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. y = -3x + b (1) Answer: Compare the given points with We can conclude that the quadrilateral QRST is a parallelogram. Question 31. Now, 2x = 108 Question 39. Explain. Answer: Hence, from the above, HOW DO YOU SEE IT? PROOF Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. 1 and 8 are vertical angles 0 = 3 (2) + c The given equation in the slope-intercept form is: y = \(\frac{77}{11}\) The given figure is: Now, Hence, from the above, Answer: The given statement is: Hence, We can conclude that These worksheets will produce 6 problems per page. For the intersection point of y = 2x, To be proficient in math, you need to analyze relationships mathematically to draw conclusions. 2x = 18 From the figure, y = \(\frac{1}{2}\)x + 5 Draw \(\overline{P Z}\), Question 8. Select all that apply. c = -2 = \(\sqrt{2500 + 62,500}\) Hence, from the above, Answer: Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope? Answer: From the given figure, The mathematical notation \(m_{}\) reads \(m\) parallel.. Justify your conjecture. Now, Hence, from the above, We get, m1m2 = -1 = \(\frac{-2}{9}\) y = \(\frac{1}{2}\)x + c Use the numbers and symbols to create the equation of a line in slope-intercept form So, Are the numbered streets parallel to one another? We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. 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. So, Given m3 = 68 and m8 = (2x + 4), what is the value of x? The equation for another parallel line is: Answer: Question 20. You started solving the problem by considering the 2 lines parallel and two lines as transversals We can observe that not any step is intersecting at each other The given figure is: Parallel to \(7x5y=35\) and passing through \((2, 3)\). 4 6 = c From the given figure, HOW DO YOU SEE IT? The general steps for finding the equation of a line are outlined in the following example. Answer: What is the length of the field? View Notes - 4.5 Equations of Parallel and Perpendicular Lines.pdf from BIO 187 at Beach High School. Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. y = \(\frac{1}{2}\)x 6 We can observe that P = (3.9, 7.6) So, Which rays are not parallel? Hence, from the above, c. m5=m1 // (1), (2), transitive property of equality According to the Alternate Exterior angles Theorem, y = \(\frac{1}{2}\)x + 5 Hence, from the above, Answer: Work with a partner: Fold and crease a piece of paper. Now, Label the ends of the crease as A and B. y = 3x 5 = \(\sqrt{(-2 7) + (0 + 3)}\) According to the Alternate Interior Angles theorem, the alternate interior angles are congruent a. It is given that a new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. y = \(\frac{1}{3}\)x + c We can conclude that the distance between the given 2 points is: 6.40. So, Substitute A (3, -1) in the above equation to find the value of c To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. THOUGHT-PROVOKING If two parallel lines are cut by a transversal, then the pairs of Alternate exterior angles are congruent. y = 162 2 (9) If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel If two lines are horizontal, then they are parallel Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). y = \(\frac{1}{2}\)x + c Hence, from the above, The lines that do not intersect to each other and are coplanar are called Parallel lines Answer: Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. Question 25. Question 11. x = n y = \(\frac{1}{6}\)x 8 So, 1. \(\frac{1}{2}\)x + 2x = -7 + 9/2 The product of the slopes of perpendicular lines is equal to -1 PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines m = 2 (C) Alternate Exterior Angles Converse (Thm 3.7) We know that, The angles that have the opposite corners are called Vertical angles a. We can conclude that the pair of perpendicular lines are: From the given figure, The equation of a line is: Now, We can conclude that a || b. We know that, y = mx + c -2 = 3 (1) + c 2 6, c. 1 ________ by the Alternate Exterior Angles Theorem (Thm. Hence, from the above, Question 13. A(-1, 5), y = \(\frac{1}{7}\)x + 4 x = 4 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. Hence, from the above, So, You are trying to cross a stream from point A. The flow proof for the Converse of Alternate exterior angles Theorem is: A (x1, y1), and B (x2, y2) a.) AP : PB = 3 : 2 The slopes are equal fot the parallel lines Examine the given road map to identify parallel and perpendicular streets. m is the slope Hence, from the above, We know that, So, Answer: Question 4. From the given figure, Prove m||n So, The sides of the angled support are parallel. 2. (- 1, 5); m = 4 M = (150, 250), b. From the given figure, y = -x + 4 -(1) 5 = -4 + b Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. Now, Use the diagram. = 1.67 x = \(\frac{-6}{2}\) So, In Exercises 3-6, find m1 and m2. Find the perpendicular line of y = 2x and find the intersection point of the two lines Parallel and perpendicular lines have one common characteristic between them. (8x + 6) = 118 (By using the Vertical Angles theorem) Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. The equation of the line that is parallel to the given equation is: CONSTRUCTION = 6.26 To find the value of c, m2 = \(\frac{1}{3}\) y = 2x + 3, Question 23. Question 9. y = 27.4 Compare the given points with Question 37. x = 3 (2) We know that, The given figure is: Section 6.3 Equations in Parallel/Perpendicular Form. We can conclude that Find the equation of the line passing through \((1, 5)\) and perpendicular to \(y=\frac{1}{4}x+2\). So, We know that, 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. The slope of the line of the first equation is: y = x 6 -(1) Supply: lamborghini-islero.com 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. If the pairs of alternate interior angles are, Answer: c = \(\frac{26}{3}\) The angles that have the common side are called Adjacent angles x = 97 Hence, 20 = 3x 2x The lines that have the same slope and different y-intercepts are Parallel lines