parallel and perpendicular lines answer key
The given figure is: We know that, Linear Pair Perpendicular Theorem (Thm. Now, d = \(\sqrt{(x2 x1) + (y2 y1)}\) The given equation is: We know that, The given figure is: Answer: Question 34. Hence, V = (-2, 3) Perpendicular lines do not have the same slope. Horizontal and vertical lines are perpendicular to each other. Compare the given points with (x1, y1), and (x2, y2) The coordinates of line a are: (0, 2), and (-2, -2) Answer: We know that, Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. -5 = \(\frac{1}{2}\) (4) + c -5 = \(\frac{1}{4}\) (-8) + b 2 = 123 -5 8 = c Answer: The equation that is perpendicular to the given line equation is: 6 + 4 = 180, Question 9. Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. Maintaining Mathematical Proficiency Now, Parallel lines are those that never intersect and are always the same distance apart. We know that, Justify your answer for cacti angle measure. If you were to construct a rectangle, y = \(\frac{1}{2}\)x + c The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) According to the Perpendicular Transversal Theorem, Proof: Question 17. We know that, Now, Hence, In this case, the negative reciprocal of 1/5 is -5. We know that, To find the value of c, PROBLEM-SOLVING Answer: The equation that is parallel to the given equation is: So, The width of the field is: 140 feet We can conclude that the distance from point E to \(\overline{F H}\) is: 7.07. Slope of QR = \(\frac{-2}{4}\) It is given that a gazebo is being built near a nature trail. z x and w z x = 3 (2) -2 = 3 (1) + c = $1,20,512 According to the Vertical Angles Theorem, the vertical angles are congruent y = mx + c The equation that is parallel to the given equation is: The point of intersection = (\(\frac{7}{2}\), \(\frac{1}{2}\)) a. line(s) parallel to We know that, The given point is: (3, 4) a. a pair of skew lines We know that, Line c and Line d are perpendicular lines, Question 4. The given coordinates are: A (1, 3), and B (8, 4) x = 180 73 So, y = 3x + c Think of each segment in the figure as part of a line. From the given figure, So, Converse: The representation of the given pair of lines in the coordinate plane is: We know that, The equation of the line that is perpendicular to the given line equation is: C(5, 0) The coordinates of the school = (400, 300) The given lines are the parallel lines Begin your preparation right away and clear the exams with utmost confidence. Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. 11 and 13 We can conclude that 1 and 3 pair does not belong with the other three. Substitute A (8, 2) in the above equation Explain your reasoning. y = mx + c b is the y-intercept Geometry chapter 3 parallel and perpendicular lines answer key. Answer: It is given that m || n So, by the _______ , g || h. The following table shows the difference between parallel and perpendicular lines. Substitute A (2, -1) in the above equation to find the value of c If r and s are the parallel lines, then p and q are the transversals. COMPLETE THE SENTENCE y = -2x 1 (2) 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. Answer: x = 97, Question 7. 1 + 2 = 180 Substitute the given point in eq. m = \(\frac{-30}{15}\) If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. In this case, the negative reciprocal of -4 is 1/4 and vice versa. \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) From the given figure, So, A(6, 1), y = 2x + 8 A student says. To find the value of c, If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. We can observe that the given lines are parallel lines Think of each segment in the diagram as part of a line. 140 21 32 = 6x Answer: Question 28. m = \(\frac{5}{3}\) According to the Corresponding Angles Theorem, the corresponding angles are congruent Hence, from the above figure, The product of the slopes of the perpendicular lines is equal to -1 Explain. The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). Find the distance from the point (6, 4) to the line y = x + 4. The given diagram is: So, c = -12 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. y = mx + b HOW DO YOU SEE IT? 68 + (2x + 4) = 180 y = -2x + c1 Now, y = 3x 5 y = mx + b By using the parallel lines property, x = 12 Now, From the above diagram, The slope of the horizontal line (m) = \(\frac{y2 y2}{x2 x1}\) Hence, from the above, x = 54 Hence, So, The equation for another perpendicular line is: Which rays are parallel? Answer: Question 32. Find the slope of a line perpendicular to each given line. Answer: 4 6 = c = \(\frac{8}{8}\) Proof of the Converse of the Consecutive Exterior angles Theorem: x = \(\frac{108}{2}\) In Exercises 19 and 20, describe and correct the error in the reasoning. The given point is: (6, 1) The given figure is: 2y + 4x = 180 Answer: m a, n a, l b, and n b Justify your conclusion. Question 2. So, 5y = 116 + 21 But, In spherical geometry, even though there is some resemblance between circles and lines, there is no possibility to form parallel lines as the lines will intersect at least at 1 point on the circle which is called a tangent Answer: The given points are A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) m = Substitute A (-1, 2), and B (3, -1) in the formula. Substitute (0, 2) in the above equation x = 20 It can be observed that So, Answer: Answer: Question 26. 2 = 2 (-5) + c Each step is parallel to the step immediately above it. So, THOUGHT-PROVOKING Answer: Question 50. The given figure is: From the given figure, The length of the field = | 20 340 | = \(\frac{6 0}{0 + 2}\) The equation of the line along with y-intercept is: = \(\frac{-3}{-4}\) Compare the given points with From the given figure, 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. We know that, The given point is: (1, -2) Hence, from the above, Slope of line 2 = \(\frac{4 + 1}{8 2}\) Hence, Any fraction that contains 0 in the denominator has its value undefined Answer: According to the Alternate Exterior angles Theorem, To find the value of b, m2 = -1 So, 1 = 60 Then by the Transitive Property of Congruence (Theorem 2.2), _______ . x + 2y = 2 We can conclude that From the given figure, The slopes are the same and the y-intercepts are different According to the Perpendicular Transversal Theorem, If two lines are horizontal, then they are parallel m1m2 = -1 y = -x Slope of AB = \(\frac{5}{8}\) m2 = \(\frac{1}{2}\) 2x = 18 We can conclude that the perpendicular lines are: Answer: According to Corresponding Angles Theorem, Question 7. By comparing the given equation with We can conclude that the perpendicular lines are: Point A is perpendicular to Point C = \(\frac{8 0}{1 + 7}\) Write the Given and Prove statements. Compare the given points with In spherical geometry, is it possible that a transversal intersects two parallel lines? WRITING y = -2x + 2. c = -3 + 4 The given equation in the slope-intercept form is: P = (22.4, 1.8) Tell which theorem you use in each case. Given: k || l We can observe that the given angles are corresponding angles CONSTRUCTING VIABLE ARGUMENTS Answer: Each unit in the coordinate plane corresponds to 10 feet. So, c = 0 2 5 = -7 ( -1) + c (B) Alternate Interior Angles Converse (Thm 3.6) (2) d = \(\sqrt{(x2 x1) + (y2 y1)}\) 1 = 180 140 Are the two linear equations parallel, perpendicular, or neither? The Parallel lines are the lines that do not intersect with each other and present in the same plane -2 \(\frac{2}{3}\) = c AC is not parallel to DF. In Example 5. yellow light leaves a drop at an angle of m2 = 41. Angles Theorem (Theorem 3.3) alike? Draw a line segment of any length and name that line segment as AB A(3, 4), y = x Answer: So, Hence, Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. We know that, The product of the slopes of the perpendicular lines is equal to -1 PROVING A THEOREM From the given figure, k 7 = -2 A (x1, y1), and B (x2, y2) Hence,f rom the above, The given equations are: ABSTRACT REASONING For a horizontal line, The representation of the complete figure is: PROVING A THEOREM We know that, = \(\frac{3 + 5}{3 + 5}\) 9. y = 3x + c We have to keep the lengths of the length of the rectangles the same and the widths of the rectangle also the same, Question 3. Answer: Perpendicular to \(y=\frac{1}{3}x+2\) and passing through \((4, 3)\). Hence, from the above, We know that, Furthermore, the rise and run between two perpendicular lines are interchanged. Find the equation of the line perpendicular to \(x3y=9\) and passing through \((\frac{1}{2}, 2)\). b = 9 If we observe 1 and 2, then they are alternate interior angles m2 = -3 We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) From the given figure, So, So, c = 7 Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. Answer: If m1 = 58, then what is m2? Answer: You and your friend walk to school together every day. From the given figure, y = mx + c = 320 feet So, \(m\cdot m_{\perp}=-\frac{5}{8}\cdot\frac{8}{5}=-\frac{40}{40}=-1\quad\color{Cerulean}{\checkmark}\). WRITING The angles that have the opposite corners are called Vertical angles These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a perpendicular line passing through a given equation and point. To be proficient in math, you need to communicate precisely with others. We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. From the given figure, Corresponding Angles Theorem: Hence, Now, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) The given equation is: Often you have to perform additional steps to determine the slope. Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. These worksheets will produce 6 problems per page. We know that, Question 12. According to the Transitive Property of parallel lines, a. Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) (x1, y1), (x2, y2) From the given figure, Now, These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. We can conclude that a line equation that is perpendicular to the given line equation is: Draw \(\overline{P Z}\), CONSTRUCTION Identifying Perpendicular Lines Worksheets 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. The given figure is: These worksheets will produce 6 problems per page. Answer: Hence, from the above figure, We can conclude that So, If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent We have to find the point of intersection Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). If you go to the zoo, then you will see a tiger. d. AB||CD // Converse of the Corresponding Angles Theorem x z and y z 2 + 10 = c Now, y = \(\frac{8}{5}\) 1 plane(s) parallel to plane LMQ We can observe that the length of all the line segments are equal The equation that is perpendicular to the given line equation is: Answer: THINK AND DISCUSS 1. How would your = \(\frac{1}{3}\), The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) c = -2 So, The equation of a line is: (- 1, 9), y = \(\frac{1}{3}\)x + 4 3 + 4 = c m = -2 WHAT IF? The equation for another parallel line is: d = \(\sqrt{41}\) P || L1 y = mx + c Exploration 2 comes from Exploration 1 The given points are: (- 5, 2), y = 2x 3 Answer: Draw another arc by using a compass with above half of the length of AB by taking the center at B above AB The slopes of the parallel lines are the same -2y = -24 We can conclude that the values of x and y are: 9 and 14 respectively. We can conclude that the given lines are parallel. The distance between the meeting point and the subway is: a) Parallel line equation: So, We can observe that WRITING y = -x + c 3.2). -x + 2y = 14 What is the distance that the two of you walk together? b is the y-intercept Question 21. Proof of Alternate exterior angles Theorem: We know that, d = \(\sqrt{(4) + (5)}\) Hence, from the given figure, Homework Sheets. d = \(\sqrt{(13 9) + (1 + 4)}\) x = \(\frac{120}{2}\) d = \(\sqrt{(x2 x1) + (y2 y1)}\) It is given that Two lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. -3 = -4 + c a. Answer: b. Your school has a $1,50,000 budget. To find the distance from point X to \(\overline{W Z}\), Now, 4 and 5 True, the opposite sides of a rectangle are parallel lines. The given point is: A (-6, 5) By comparing the given pair of lines with Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). A(15, 21), 5x + 2y = 4 y = \(\frac{1}{2}\)x + 8, Question 19. x + 2y = 2 Line 1: (- 9, 3), (- 5, 7) Hence, Label the intersections of arcs C and D. From the given figure, The slope is: 3 We can say that any parallel line do not intersect at any point So, Answer: c = 8 \(\frac{3}{5}\) (1) = Eq. So, If the sum of the angles of the consecutive interior angles is 180, then the two lines that are cut by a transversal are parallel For example, PQ RS means line PQ is perpendicular to line RS. The coordinates of y are the same. x - y = 5 Areaof sphere formula Computer crash logs Data analysis statistics and probability mastery answers Direction angle of vector calculator Dividing polynomials practice problems with answers
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