m = \(\frac{-2}{7 k}\) We can conclude that the parallel lines are: x = \(\frac{153}{17}\) 3.12) In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. Compare the given coordinates with Now, Hence, from the given figure, = \(\frac{8 0}{1 + 7}\) Compare the given points with XY = 4.60 Will the opening of the box be more steep or less steep? y = \(\frac{1}{3}\)x + c If two angles form a linear pair. The diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal Use the numbers and symbols to create the equation of a line in slope-intercept form Now, We can conclude that x and y are parallel lines, Question 14. So, Now, So, The sum of the given angle measures is: 180 AP : PB = 2 : 6 This line is called the perpendicular bisector. So, The slopes of the parallel lines are the same 5 = -4 + b Substitute (-1, -1) in the above equation The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, The rope is pulled taut. Answer: Question 12. Question 1. 8 = -2 (-3) + b We know that, 3 = 68 and 8 = (2x + 4) We know that, The Intersecting lines are the lines that intersect with each other and in the same plane Hence, from the above, y = \(\frac{1}{4}\)x + 4, Question 24. Answer: Question 24. x + 2y = 2 The slope of the equation that is perpendicular to the given equation is: \(\frac{1}{m}\) Grade: Date: Parallel and Perpendicular Lines. The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines 2 and 3 are the consecutive interior angles We know that, y = mx + c Question 14. 2 = 0 + c k = 5 Now, The equation of the line that is parallel to the line that represents the train tracks is: The line y = 4 is a horizontal line that have the straight angle i.e., 0 Answer: Answer: y = -x, Question 30. c = 2 1 The equation of the parallel line that passes through (1, 5) is: Answer: We have seen that the graph of a line is completely determined by two points or one point and its slope. HOW DO YOU SEE IT? Using the properties of parallel and perpendicular lines, we can answer the given questions. We can conclude that the value of x is: 14.
4.05: Parallel and Perpendicular Lines Flashcards | Quizlet We can conclude that the claim of your classmate is correct. a) Parallel line equation: 10) Slope of Line 1 12 11 . We can conclude that the distance from the given point to the given line is: \(\frac{4}{5}\). Answer: The Alternate Interior angles are congruent So, Answer: The given point is: P (4, -6) From the given figure, c = -5 y = \(\frac{3}{2}\)x + 2 Substitute (-5, 2) in the above equation From the given figure, a. Substitute (-1, -9) in the above equation The slope of the given line is: m = \(\frac{1}{4}\) The equation of the line along with y-intercept is: Answer: Question 6. Hence, From the given coordinate plane, The given figure is: (x + 14)= 147 c = \(\frac{8}{3}\) y = \(\frac{1}{6}\)x 8 x and 97 are the corresponding angles For a horizontal line, So, Which lines are parallel to ? For example, the opposite sides of a square and a rectangle have parallel lines in them, and the adjacent lines in the same shapes are perpendicular lines. The given equation is: P(3, 8), y = \(\frac{1}{5}\)(x + 4) In Exercises 3 and 4. find the distance from point A to . We know that, Explain your reasoning. -4 = -3 + c \(m_{}=10\) and \(m_{}=\frac{1}{10}\), Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines. Verticle angle theorem: y = \(\frac{1}{2}\)x 7 y 500 = -3x + 150 A (x1, y1), B (x2, y2) (- 5, 2), y = 2x 3 Solve eq. a. a pair of skew lines Answer: We know that, (50, 500), (200, 50) How do you know that the lines x = 4 and y = 2 are perpendiculars? We can conclude that b || a, Question 4. Answer: The given figure is: x = 4 We can observe that, Write the equation of the line that is perpendicular to the graph of 6 2 1 y = x + , and whose y-intercept is (0, -2). y = \(\frac{3}{2}\)x + 2, b. Answer: From the given figure, Answer: Compare the given points with Compare the given equation with Hence, from the above, P = (7.8, 5) Parallel to \(y=\frac{3}{4}x+1\) and passing through \((4, \frac{1}{4})\). 2x = 18 A (-1, 2), and B (3, -1) Question 4. Work with a partner: The figure shows a right rectangular prism. The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. P( 4, 3), Q(4, 1) In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. b. m1 + m4 = 180 // Linear pair of angles are supplementary
Parallel and Perpendicular Lines Worksheet (with Answer Key) From the given figure, \(\frac{5}{2}\)x = \(\frac{5}{2}\) We can conclude that FCA and JCB are alternate exterior angles. Proof: The distance between the two parallel lines is: The pair of lines that are different from the given pair of lines in Exploration 2 are: The given figure is: = \(\sqrt{(6) + (6)}\) Converse: 2 and 3 are vertical angles 4x = 24 Now, Draw \(\overline{P Z}\), CONSTRUCTION We can conclude that the value of x when p || q is: 54, b. We know that, = 255 yards The given coordinates are: A (-2, 1), and B (4, 5) BCG and __________ are consecutive interior angles. -9 = 3 (-1) + c The given lines are the parallel lines We can conclude that So, Proof of the Converse of the Consecutive Interior angles Theorem: \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). The given figure is: \(\frac{1}{2}\)x + 1 = -2x 1 The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent = \(\frac{-2 2}{-2 0}\) Answer: Hence, from the above, According to the Perpendicular Transversal Theorem, -3 = 9 + c The postulates and theorems in this book represent Euclidean geometry. Question 33. y = x 6 -(1) We can conclude that the distance from point A to \(\overline{X Z}\) is: 4.60. From the given figure, 1. The lines that have the same slope and different y-intercepts are Parallel lines We know that, 3y = x + 475 _____ lines are always equidistant from each other. Compare the given equations with No, your friend is not correct, Explanation: Parallel to \(x+y=4\) and passing through \((9, 7)\). It is given that P = (3.9, 7.6) y = \(\frac{1}{2}\)x + 2 -2 = 1 + c Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. It is given that a student claimed that j K, j l When two lines are crossed by another line (which is called the Transversal), theangles in matching corners are called Corresponding angles Step 4: P(4, 0), x + 2y = 12 We can observe that The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) So, We can conclude that the slope of the given line is: \(\frac{-3}{4}\), Question 2. The given equation is: Hence, from the above, Answer: So, The given point is: (3, 4) m = 2 The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. The slopes are equal fot the parallel lines If we see a few real-world examples, we can notice parallel lines in them, like the opposite sides of a notebook or a laptop, represent parallel lines, and the intersecting sides of a notebook represent perpendicular lines. If you go to the zoo, then you will see a tiger In Exercises 19 and 20, describe and correct the error in the reasoning. Question 23. c1 = 4 We can conclude that the value of x is: 12, Question 10. We know that, A(2, 1), y = x + 4 \(m_{}=\frac{5}{8}\) and \(m_{}=\frac{8}{5}\), 7. The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) So, We have to find the point of intersection The given figure is: 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. The given point is: (-1, 6) Now, Now, m1m2 = -1 From the given figure, We know that, From the above figure, For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts We know that, The slope is: 3 5x = 149 The coordinates of the line of the second equation are: (-4, 0), and (0, 2) y = \(\frac{1}{7}\)x + 4 We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. = \(\frac{-4}{-2}\) P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Explain why or why not. lines intersect at 90. ANALYZING RELATIONSHIPS What are Parallel and Perpendicular Lines? By the _______ . Compare the given points with (x1, y1), (x2, y2) The opposite sides of a rectangle are parallel lines. 8 6 = b We can conclude that p and q; r and s are the pairs of parallel lines. The given equation is: What is the distance that the two of you walk together? So, Prove: t l It is given that m || n y = \(\frac{1}{2}\)x + c So, We know that, The postulates and theorems in this book represent Euclidean geometry. Question 27. The slope of the given line is: m = \(\frac{1}{2}\) To find the value of c, The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) The line parallel to \(\overline{E F}\) is: \(\overline{D H}\), Question 2. Compare the given points with (x1, y1), and (x2, y2) We can conclude that 18 and 23 are the adjacent angles, c. d = \(\sqrt{(x2 x1) + (y2 y1)}\) THOUGHT-PROVOKING y = 144 Question 27. How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior The slopes are equal fot the parallel lines \(\overline{C D}\) and \(\overline{A E}\) are Skew lines because they are not intersecting and are non coplanar y = \(\frac{1}{2}\)x 3, b. FSE = ESR Answer the questions related to the road map. Alternate Exterior Angles Theorem: Answer: The equation of line p is: We know that,
PDF Parallel and Perpendicular Lines : Shapes Sheet 1 - Math Worksheets 4 Kids Answer: m is the slope Question 12. So, = \(\frac{6 0}{0 + 2}\) To find the coordinates of P, add slope to AP and PB The given point is: P (4, 0) Answer: Question 29. Now, ANALYZING RELATIONSHIPS Answer: Answer:
Which rays are not parallel?
Parallel And Perpendicular Lines Worksheet Answers Key - pdfFiller