parallel and perpendicular lines answer key

= \(\frac{2}{-6}\) A (x1, y1), B (x2, y2) So, (2, 4); m = \(\frac{1}{2}\) The angles formed at all the intersection points are: 90 The length of the field = | 20 340 | = \(\frac{8 0}{1 + 7}\) We can conclude that The slope of perpendicular lines is: -1 Work with a partner: Write the converse of each conditional statement. The given figure is: b. So, Compare the given points with b = 9 Hw Key Hw Part 2 key Updated 9/29/22 #15 - Perpendicular slope 3.6 (2017) #16 - Def'n of parallel 3.1 . Hence, from the given figure, A gazebo is being built near a nature trail. Compare the given points with (x1, y1), (x2, y2) y = \(\frac{1}{5}\)x + \(\frac{37}{5}\) Use a graphing calculator to verify your answer. We know that, y = 2x + c2, b. = \(\frac{-2}{9}\) Answer: The lines that do not have any intersection points are called Parallel lines The given figure is: Answer: Hence, from the above, We know that, Prove m||n x = 2 If you will see a tiger, then you go to the zoo-> False. So, For a vertical line, Question 1. Hence, from the above, a. Hence, from the above, Question 5. = (\(\frac{-5 + 3}{2}\), \(\frac{-5 + 3}{2}\)) Lines AB and CD are not intersecting at any point and are always the same distance apart. x = 54 Answer: Hence, Work with a partner: Fold and crease a piece of paper. If the pairs of corresponding angles are, congruent, then the two parallel lines are. We know that, 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 We can observe that the plane parallel to plane CDH is: Plane BAE. m1 = m2 = \(\frac{3}{2}\) m = 2 Which line(s) or plane(s) contain point B and appear to fit the description? In Exercises 13 and 14, prove the theorem. Answer: 5y = 116 + 21 Answer: y = \(\frac{1}{2}\)x + 1 -(1) y = \(\frac{1}{3}\) (10) 4 The given figure is: Here is a quick review of the point/slope form of a line. y = mx + c m = \(\frac{1}{4}\) m = = So, slope of the given line is Question 2. Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) a. y = 4x + 9 The representation of the perpendicular lines in the coordinate plane is: Question 19. Find the equation of the line passing through \((6, 1)\) and parallel to \(y=\frac{1}{2}x+2\). Answer: Hence, from the above, Hence, Answer: (13, 1) and (9, 4) Homework Sheets. Explain your reasoning. = \(\sqrt{(-2 7) + (0 + 3)}\) Hence, from the above, Two lines are cut by a transversal. Now, y = \(\frac{1}{2}\)x 3 x = 60 So, The product of the slopes of the perpendicular lines is equal to -1 Compare the above equation with . m1m2 = -1 We know that, Two lines are termed as parallel if they lie in the same plane, are the same distance apart, and never meet each other. The slopes of the parallel lines are the same x 2y = 2 We know that, Using X as the center, open the compass so that it is greater than half of XP and draw an arc. We can observe that We can conclude that So, Hence, We were asked to find the equation of a line parallel to another line passing through a certain point. Now, y = \(\frac{2}{3}\)x + 1 Answer: Question 2. The given point is: A (-1, 5) You and your mom visit the shopping mall while your dad and your sister visit the aquarium. Draw an arc with center A on each side of AB. The slope of first line (m1) = \(\frac{1}{2}\) Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive Hence, 2x y = 4 Parallel to \(y=3\) and passing through \((2, 4)\). We know that, So, by the Corresponding Angles Converse, g || h. Question 5. b. To find the value of c, 12. = \(\sqrt{(250 300) + (150 400)}\) 10) Slope of Line 1 12 11 . Substitute the given point in eq. Answer: Justify your conclusion. Is b c? Each unit in the coordinate plane corresponds to 50 yards. d = \(\sqrt{(x2 x1) + (y2 y1)}\) The best editor is directly at your fingertips offering you a range of advantageous instruments for submitting a Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines. We can conclude that the values of x and y are: 9 and 14 respectively. We know that, In Exercise 40 on page 144, You are designing a box like the one shown. Is your friend correct? Now, We know that, a. y = \(\frac{1}{2}\)x + c d = | ax + by + c| /\(\sqrt{a + b}\) 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. The equation that is perpendicular to the given line equation is: In Exploration 2. find more pairs of lines that are different from those given. (11x + 33)+(6x 6) = 180 c = -9 3 Question 30. An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. Answer: c = 1 The lengths of the line segments are equal i.e., AO = OB and CO = OD. Select the angle that makes the statement true. = \(\frac{-3}{4}\) Hence, from the above, = \(\frac{-4}{-2}\) We know that, d = \(\sqrt{(300 200) + (500 150)}\) Answer: We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6. CONSTRUCTION If the slope of one is the negative reciprocal of the other, then they are perpendicular. Prove c||d The coordinates of line c are: (2, 4), and (0, -2) d = | x y + 4 | / \(\sqrt{2}\)} 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. The given point is: (0, 9) c1 = 4 y = \(\frac{1}{6}\)x 8 Answer: Question 30. y = -x + c 7x = 108 24 Prove: c || d y = 27.4 The given figure is: The slopes are equal fot the parallel lines Hence, (A) Corresponding Angles Converse (Thm 3.5) The Perpendicular lines are the lines that are intersected at the right angles We can observe that, Which lines intersect ? From the above figure, COMPLETE THE SENTENCE y = \(\frac{1}{3}\)x + c When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90, Work with a partner. We can conclude that the parallel lines are: We can observe that the angle between b and c is 90 b is the y-intercept x = -1 1 = 53.7 and 5 = 53.7 No, your friend is not correct, Explanation: By the _______ . b. In Exploration 1, explain how you would prove any of the theorems that you found to be true. We know that, Proof of the Converse of the Consecutive Interior angles Theorem: Answer: USING STRUCTURE \(\frac{1}{2}\) (m2) = -1 d. AB||CD // Converse of the Corresponding Angles Theorem Hence, from the above, Answer: Question 26. Slope of AB = \(\frac{5 1}{4 + 2}\) We can say that any parallel line do not intersect at any point From the given figure, So, \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines We can conclude that FCA and JCB are alternate exterior angles. We know that, a. c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem. We can conclude that b is perpendicular to c. Question 1. c = 0 Now, y = -x -(1) y = -3x + 19, Question 5. Answer: No, the third line does not necessarily be a transversal, Explanation: We can observe that y = -x 12 (2) The given line has the slope \(m=\frac{1}{7}\), and so \(m_{}=\frac{1}{7}\). Now, When we compare the converses we obtained from the given statement and the actual converse, Answer: Question 40. The lines that have the same slope and different y-intercepts are Parallel lines Answer: Answer: Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. x = 14.5 -5 8 = c Given 1 3 The given equation is: b. Alternate Exterior angles Theorem Hence, from the above, Answer: Step 1: The area of the field = Length Width The given figure is: 8x and (4x + 24) are the alternate exterior angles J (0 0), K (0, n), L (n, n), M (n, 0) y = \(\frac{1}{4}\)x 7, Question 9. Now, Now, E (x1, y1), G (x2, y2) It is given that m || n Substitute P (4, -6) in the above equation : n; same-side int. 8 = 65 3 = 180 133 We have seen that the graph of a line is completely determined by two points or one point and its slope. The line l is also perpendicular to the line j The coordinates of line d are: (-3, 0), and (0, -1) Answer: The Alternate Interior angles are congruent x y = 4 Answer: which ones? Yes, your classmate is correct, Explanation: The product of the slopes of perpendicular lines is equal to -1 Answer: Question 18. In this case, the negative reciprocal of 1/5 is -5. The perpendicular lines have the product of slopes equal to -1 k = 5 Substitute P (3, 8) in the above equation to find the value of c Your school lies directly between your house and the movie theater. So, So, Proof: So, We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. \(\frac{8-(-3)}{7-(-2)}\) The equation of the line that is perpendicular to the given line equation is: We know that, Parallel to \(x+4y=8\) and passing through \((1, 2)\). y = mx + c By comparing the given pair of lines with So, The given point is: (6, 1) 4 ________ b the Alternate Interior Angles Theorem (Thm. = 2 (320 + 140) Answer: Which type of line segment requires less paint? There are some letters in the English alphabet that have both parallel and perpendicular lines. y = \(\frac{1}{2}\)x + 7 Hence, from the above, We know that, b. Step 5: The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) y = x + 9 To find the value of b, y = x 3 (2) answer choices Parallel Perpendicular Neither Tags: MGSE9-12.G.GPE.5 Question 7 300 seconds PDF Name: Unit 3: Parallel & Perpendicular Lines Bell: Homework 5: Linear. We can observe that Answer: Explain Your reasoning. In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? We know that, From the given figure, All the angles are right angles. Answer: Hence, from the above, Answer: The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. 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. ABSTRACT REASONING Explain your reasoning. Question 13. Hence, from the above, We can conclude that the perpendicular lines are: The given coordinates are: A (-2, 1), and B (4, 5) The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line The Converse of the alternate exterior angles Theorem: Answer: In Exercises 17-22, determine which lines, if any, must be parallel. If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. (- 1, 9), y = \(\frac{1}{3}\)x + 4 XY = \(\sqrt{(3 + 3) + (3 1)}\) Start by finding the parallels, work on some equations, and end up right where you started. Compare the given equations with The equation that is perpendicular to the given line equation is: We can observe that the given lines are perpendicular lines Question 29. THOUGHT-PROVOKING Parallel to \(x=2\) and passing through (7, 3)\). = \(\frac{-3}{-1}\) Now, The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar From the given figure, Answer: 9 and x- Answer: 2 and y Answer: x +15 and Answer: x +10 2 x -6 and 2x + 3y Answer: 6) y and 3x+y=- Answer: Answer: 14 and y = 5 6 (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. d = 6.40 Slope (m) = \(\frac{y2 y1}{x2 x1}\) From the above table, They are not parallel because they are intersecting each other. Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. Compare the given points with (x1, y1), and (x2, y2) b.) c = -6 We know that, We can conclude that MATHEMATICAL CONNECTIONS You and your friend walk to school together every day. Repeat steps 3 and 4 below AB The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Answer: WRITING Compare the given coordinates with According to the Corresponding Angles Theorem, the corresponding angles are congruent then they are supplementary.