XZ = \(\sqrt{(7) + (1)}\) When we compare the converses we obtained from the given statement and the actual converse, Answer: Question 26. If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. From the figure, To find an equation of a line, first use the given information to determine the slope. Use the numbers and symbols to create the equation of a line in slope-intercept form So, We can observe that we divided the total distance into the four congruent segments or pieces Hence, REASONING You and your mom visit the shopping mall while your dad and your sister visit the aquarium. We know that, Intersecting lines can intersect at any . We can conclude that a line equation that is perpendicular to the given line equation is: 2x = 3 ax + by + c = 0 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 know that, ATTENDING TO PRECISION We can conclude that Answer: Question 2. d = \(\sqrt{41}\) Question 12. = \(\frac{8}{8}\) The slopes of perpendicular lines are undefined and 0 respectively It is given that m || n Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(1: m1m2=1\). Hence, from the above, Vertical Angles are the anglesopposite each other when two lines cross Answer: = \(\frac{-1 0}{0 + 3}\) The slopes are equal fot the parallel lines Hence, from the above figure, Answer: an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). Some examples follow. Question 47. Answer: = \(\frac{-3}{4}\) C(5, 0) Slope of AB = \(\frac{5 1}{4 + 2}\) y = 145 The bottom step is parallel to the ground. Identify all pairs of angles of the given type. We know that, The equation that is perpendicular to y = -3 is: y = -x 12 (2) Substitute the given point in eq. = \(\frac{-6}{-2}\) From the given bars, y = 4x + b (1) 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. (- 1, 9), y = \(\frac{1}{3}\)x + 4 Ruler: The highlighted lines in the scale (ruler) do not intersect or meet each other directly, and are the same distance apart, therefore, they are parallel lines. m = 2 are parallel, or are the same line. Answer: 90 degrees (a right angle) That's right, when we rotate a perpendicular line by 90 it becomes parallel (but not if it touches!) Hence, from the above, Answer: ERROR ANALYSIS If you will go to the park, then it is warm outside -> False. The given figure is: Corresponding Angles Theorem So, The given equation is: The diagram of the control bar of the kite shows the angles formed between the Control bar and the kite lines. y = mx + c The given figure is: Answer: \(\overline{D H}\) and \(\overline{F G}\) Find the value of x when a b and b || c. Describe and correct the error in the students reasoning 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 y = -x + c = 0 (4.3.1) - Parallel and Perpendicular Lines - Lumen Learning Answer: It is given that 1 = 58 Answer: -5 = 2 (4) + c Do you support your friends claim? It is given that a student claimed that j K, j l Now, What conjectures can you make about perpendicular lines? x = \(\frac{149}{5}\) Which pair of angle measures does not belong with the other three? Using X and Y as centers and an appropriate radius, draw arcs that intersect. The given figure is: Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). From the given figure, The angle measures of the vertical angles are congruent

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