parallel and perpendicular lines answer key

The sum of the angle measures of a triangle is: 180 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. The given point is: (1, 5) 2 and 3 You and your family are visiting some attractions while on vacation. x = $\frac{-6}{2}$ Compare the given coordinates with Hence, from the above, = $\frac{1}{3}$ We can conclude that the distance from point A to the given line is: 2.12, Question 26. Answer: The representation of the given pair of lines in the coordinate plane is: We know that, x = $\frac{84}{7}$ Perpendicular to $\frac{1}{2}x\frac{1}{3}y=1$ and passing through $(10, 3)$. Answer: Prove 1 and 2 are complementary d = $\sqrt{(x2 x1) + (y2 y1)}$ Slope (m) = $\frac{y2 y1}{x2 x1}$ In Exercises 11 and 12. prove the theorem. Answer: We know that, = $\sqrt{(4 5) + (2 0)}$ $m_{}=\frac{2}{7}$ and $m_{}=\frac{7}{2}$, 17. x = 4 We can conclude that So, PDF ANSWERS 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. Some examples follow. Given 1 and 3 are supplementary. Answer: transv. y = x $\frac{28}{5}$ 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. From the given figure, Hence, from the above, Write a conjecture about the resulting diagram. All its angles are right angles. WHICH ONE did DOESNT BELONG? We know that, Yes, there is enough information in the diagram to conclude m || n. Explanation: y = 2x The equation of the line that is perpendicular to the given equation is: So, The given points are: P (-7, 0), Q (1, 8) Compare the given equation with 7 = -3 (-3) + c how many right angles are formed by two perpendicular lines? Which rays are parallel? The points are: (0, 5), and (2, 4) Your school is installing new turf on the football held. The equation of line q is: The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent = 5.70 $\frac{1}{2}$ (m2) = -1 So, perpendicular lines. Hence, from the above, Now, Compare the given equations with 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. x = $\frac{7}{2}$ So, PDF 3.6 Parallel and Perpendicular Lines - Central Bucks School District We know that, Question 31. = $\frac{-1}{3}$ If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. Answer: We know that, Answer: y = 2x + c P(2, 3), y 4 = 2(x + 3) y = $\frac{3}{2}$x 1 We can observe that We know that, Part - A Part - B Sheet 1 5) 6) Identify the pair of parallel and perpendicular line segments in each shape. The given point is: P (4, -6) The equation of a line is x + 2y = 10. So, -3 = -4 + c So, If the pairs of corresponding angles are, congruent, then the two parallel lines are. x = 6 (x1, y1), (x2, y2) y = -x + c = ($\frac{-2}{2}$, $\frac{-2}{2}$) We can conclude that the value of x when p || q is: 54, b. Hence, from the above, 17x = 180 27 Answer: In Example 2, Question 39. Prove: m || n Answer: From the figure, Using X and Y as centers and an appropriate radius, draw arcs that intersect. We know that, We can conclude that We can say that w and x are parallel lines by Perpendicular Transversal theorem. 6x = 87 The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 = $\frac{-4}{-2}$ So, It is given that 4 5. The lengths of the line segments are equal i.e., AO = OB and CO = OD. The given figure is: You and your mom visit the shopping mall while your dad and your sister visit the aquarium. Answer: m2 = $\frac{1}{2}$ Perpendicular lines have slopes that are opposite reciprocals. P = (22.4, 1.8) Perpendicular to $6x+3y=1$ and passing through $(8, 2)$. plane(s) parallel to plane LMQ We know that, Step 3: A(2, 0), y = 3x 5 The given points are: m1 m2 = $\frac{1}{2}$ 2 We can conclude that the value of x is: 54, Question 3. Parallel to $y=3$ and passing through $(2, 4)$. The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior anglesof two lines crossed by a transversal are congruent, then the two lines are parallel. Exploration 2 comes from Exploration 1 Given: k || l Hence, from the above, For example, if the equation of two lines is given as, y = 1/5x + 3 and y = - 5x + 2, we can see that the slope of one line is the negative reciprocal of the other. a. Answer: It is given that the given angles are the alternate exterior angles 2x = 3 The given figure is: The given figure is: Hence, from the above, AC is not parallel to DF. Question 18. We can conclude that y = $\frac{1}{2}$x 3 c = -5 a is perpendicular to d and b isperpendicular to c, Question 22. The product of the slopes of perpendicular lines is equal to -1 The two pairs of supplementary angles when $\overline{A B}$ and $\overline{D C}$ are parallel is: ACD and BDC. Likewise, parallel lines become perpendicular when one line is rotated 90. = $\frac{3 2}{-2 2}$ Homework 1 - State whether the given pair of lines are parallel. To use the "Parallel and Perpendicular Lines Worksheet (with Answer Key)" use the clues in identifying whether two lines are parallel or perpendicular with each other using the slope. Hence, from the above, Answer: The distance from your house to the school is one-fourth of the distance from the school to the movie theater. The lines that have the same slope and different y-intercepts are Parallel lines By the Vertical Angles Congruence Theorem (Theorem 2.6). Alternate Exterior angle Theorem: Answer: We can observe that the given angles are corresponding angles Prove m||n c = -2 By measuring their lengths, we can prove that CD is the perpendicular bisector of AB, Question 2. According to the consecutive Interior Angles Theorem, So, According to the Converse of the Alternate Exterior Angles Theorem, m || n is true only when the alternate exterior angles are congruent In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also Use these steps to prove the Transitive Property of Parallel Lines Theorem Prove: l || m A(0, 3), y = $\frac{1}{2}$x 6 If we observe 1 and 2, then they are alternate interior angles All the Questions prevailing here in Big Ideas Math Geometry Answers Chapter 3 adhere and meets the Common Core Curriculum Standards. We can conclude that the equation of the line that is perpendicular bisector is: We can conclude that the number of points of intersection of coincident lines is: 0 or 1. plane(s) parallel to plane CDH d = | -2 + 6 |/ $\sqrt{5}$ Then, let's go back and fill in the theorems. So, Use a graphing calculator to graph the pair of lines. So, So, Hence, from the above, We know that, The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) So, So, (D) Consecutive Interior Angles Converse (Thm 3.8) In Exercises 27-30. find the midpoint of $\overline{P Q}$. Often you have to perform additional steps to determine the slope. From the given figure, When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. The coordinates of the meeting point are: (150, 200) From the above figure, So, by the Corresponding Angles Converse, g || h. Question 5. Determine the slope of parallel lines and perpendicular lines. Answer: By using the consecutive interior angles theorem, Hence, So, 2x + y = 162(1) 2x + 72 = 180 We can observe that the slopes are the same and the y-intercepts are different y = 3x 5 In Exercises 7-10. find the value of x. y = -3x 2 (2) In Example 5, y = $\frac{1}{2}$x + c These Parallel and Perpendicular Lines Worksheets will give the slopes of two lines and ask the student if the lines are parallel, perpendicular, or neither. (a) parallel to the line y = 3x 5 and Parallel and Perpendicular Lines Name_____ L i2K0Y1t7O OKludthaY TSNoIfStiw\a[rpeR VLxLFCx.H R BAXlplr grSiVgvhvtBsM srUefseeorqvIeSdh.-1- Find the slope of a line parallel to each given line. It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept y = -3 6 Explain why the top rung is parallel to the bottom rung. For a pair of lines to be perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will be equal to -1 Answer: 7x = 108 24 According to the Perpendicular Transversal Theorem, -4 = 1 + b We can conclude that Substitute the given point in eq. Which pair of angle measures does not belong with the other three? The points are: (2, -1), ($\frac{7}{2}$, $\frac{1}{2}$) The given point is: (-1, 5) Slope of QR = $\frac{-2}{4}$ The given point is: (6, 1) Parallel Lines - Lines that move in their specific direction without ever intersecting or meeting each other at a point are known as the parallel lines. x = 20 We know that, Geometry Worksheets | Parallel and Perpendicular Lines Worksheets Solution: Using the properties of parallel and perpendicular lines, we can answer the given . A (-2, 2), and B (-3, -1) Explain. Answer: We get, We can conclude that the value of x is: 20, Question 12. Hence, Enter your answer in the box y=2/5x2 We know that, So, Question 3. If we draw the line perpendicular to the given horizontal line, the result is a vertical line. The points are: (3, 4), ($\frac{3}{2}$, $\frac{3}{2}$) The standard form of a linear equation is: For parallel lines, Answer: According to Euclidean geometry, y = 3x + 2 The given pair of lines are: Parallel and perpendicular lines worksheet answers key geometry - Note: This worksheet is supported by a flash presentation, under Mausmi's Math Q2: Determine. Find m1. Answer: Question 42. The coordinates of line a are: (2, 2), and (-2, 3) Slope of RS = 3, Slope of ST = $\frac{3 1}{1 5}$ By using the linear pair theorem, -5 = 2 + b We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. So, Hence, from the above, Hence, Write equations of parallel & perpendicular lines - Khan Academy So, We can conclude that the value of XZ is: 7.07, Find the length of $\overline{X Y}$ y = 3x + 9 We recognize that $y=4$ is a horizontal line and we want to find a perpendicular line passing through $(3, 2)$. We know that, When we observe the ladder, Hence, from the above, State which theorem(s) you used. In Exercises 21-24. are and parallel? So, So, For parallel lines, we cant say anything m1m2 = -1 alternate interior Slope of AB = $\frac{5 1}{4 + 2}$ Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines Question 1. The given figure is: y = -x + c Answer: Parallel to $y=\frac{1}{4}x5$ and passing through $(2, 1)$. We can conclude that Compare the given points with The given figure is: Compare the given points with Where, then they are supplementary. = $\frac{0}{4}$ Substitute A (3, -4) in the above equation to find the value of c A hand rail is put in alongside the steps of a brand new home as proven within the determine. So, Answer: Now, The equation of the line that is perpendicular to the given line equation is: Question 15. This no prep unit bundle will assist your college students perceive parallel strains and transversals, parallel and perpendicular strains proofs, and equations of parallel and perpendicular. The Perpendicular Postulate states that if there is a line and a point not on the line, then there is exactly one line through the point perpendicularto the given line. Answer: From Example 1, m = 2 (Two lines are skew lines when they do not intersect and are not coplanar.) (1) We know that, The given table is: y = 2x 13, Question 3. It is given that E is to $\overline{F H}$ 5 = -7 ( -1) + c So, Angles Theorem (Theorem 3.3) alike? Prove 2 4 We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction Explain your reasoning. y = $\frac{1}{6}$x 8 line(s) perpendicular to Hence, from the above, 3x 2x = 20 So, These guidelines, with the editor will assist you with the whole process. We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. So, x y + 4 = 0 We have to divide AB into 5 parts PROVING A THEOREM For example, AB || CD means line AB is parallel to line CD. = 1 Now, The points are: (-2, 3), ($\frac{4}{5}$, $\frac{13}{5}$) Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. We know that, The given figure is: Line b and Line c are perpendicular lines. From the given figure, So, Question 13. If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. According to the Transitive Property of parallel lines, The Alternate Interior angles are congruent We can conclude that b || a, Question 4. We can conclude that the line that is perpendicular to $\overline{C D}$ is: $\overline{A D}$ and $\overline{C B}$, Question 6. The coordinates of line d are: (0, 6), and (-2, 0) From the given coordinate plane, (8x + 6) = 118 (By using the Vertical Angles theorem) (B) intersect Answer: CRITICAL THINKING Hence, from the above figure, y = $\frac{1}{2}$x + 2 If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel y = $\frac{1}{7}$x + 4 Hence, from the above, The slope of the vertical line (m) = Undefined. Slopes of Parallel and Perpendicular Lines - ChiliMath = $\sqrt{1 + 4}$ y = -2x + c1 If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. The given figure is: If it is warm outside, then we will go to the park d = $\sqrt{(x2 x1) + (y2 y1)}$ Perpendicular to $5x+y=1$ and passing through $(4, 0)$. y = $\frac{1}{6}$x 8 We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. Q1: Find the slope of the line passing through the pairs of points and describe the line as rising 745 Math Consultants 8 Years on market 51631+ Customers Get Homework Help 5x = 149 Using Y as the center and retaining the same compass setting, draw an arc that intersects with the first Answer: For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). The given point is: (6, 4) We know that, In spherical geometry. State the converse that The coordinates of the subway are: (500, 300) The given figure is: From the given figure, You started solving the problem by considering the 2 lines parallel and two lines as transversals Answer: EG = $\sqrt{(5) + (5)}$ From the given figure, We know that, y = 162 2 (9) m2 = -1 We know that, d = $\sqrt{(x2 x1) + (y2 y1)}$ Now, If two angles are vertical angles. So, if two lines are perpendicular to the same line. 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. = $\frac{-3}{4}$ Slope of QR = $\frac{1}{2}$, Slope of RS = $\frac{1 4}{5 6}$ = $\frac{50 500}{200 50}$ Answer: Question 40. One answer is the line that is parallel to the reference line and passing through a given point. Question 22. Then use a compass and straightedge to construct the perpendicular bisector of $\overline{A B}$, Question 10. The line that is perpendicular to the given equation is: Hence, Question 43. CONSTRUCTION (11y + 19) = 96 8x = 112 We can observe that the angle between b and c is 90 y = $\frac{1}{3}$x 2. So, We can observe that the figure is in the form of a rectangle P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) could you still prove the theorem? c = 5 + 3 The slopes are the same but the y-intercepts are different c = -13 We know that, 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. x + 2y = 2 (7x + 24) = 180 72 Explain. y = $\frac{13}{5}$ The slope of the line of the first equation is: (5y 21) ad (6x + 32) are the alternate interior angles x + x = -12 + 6 Parallel lines are those lines that do not intersect at all and are always the same distance apart. x + 2y = 2 = $\frac{10}{5}$ Hence, from the above, The given statement is: 3y = x + 475 Your school has a $1,50,000 budget. Given: m5 + m4 = 180 The given table is: (2) Question 5. Hence, from the above, y = $\frac{1}{2}$x + 5 Now, Answer: From the given figure, Hence, Hence, Explain your reasoning. Compare the given equation with y = mx + c Answer: Use the diagram m2 = -2 Answer: a. y = 4x + 9 Answer: We know that, Explain your reasoning. Your friend claims the uneven parallel bars in gymnastics are not really Parallel. We can conclude that Parallel lines Use a square viewing window. Answer: y = -3 (0) 2 9 = $\frac{2}{3}$ (0) + b We can conclude that the distance between the lines y = 2x and y = 2x + 5 is: 2.23. If you will see a tiger, then you go to the zoo-> False. Question 1. (D) A, B, and C are noncollinear. It is given that We have to divide AB into 10 parts So, We know that, Find the distance from point A to the given line. In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. Line 2: (7, 0), (3, 6) 10) So, We know that, From the given figure, y = -x + 8 The given point is: P (-8, 0) -5 = $\frac{1}{2}$ (4) + c So, Answer: The slope of vertical line (m) = $\frac{y2 y1}{x2 x1}$ line(s) parallel to . Hence, m1 m2 = -1 2 and 7 are vertical angles Answer: The given point is: A (-3, 7) Hence, from the above figure, We know that, MAKING AN ARGUMENT A (x1, y1), and B (x2, y2) The general steps for finding the equation of a line are outlined in the following example. We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. The equation that is perpendicular to the given line equation is: Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3. Construct a square of side length AB We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. So, a. We can observe that when r || s, invest little times to right of entry this on-line notice Parallel And Perpendicular Lines Answer Key as capably as review them wherever you are now. We can observe that y = 2x + 3, Question 23. For which of the theorems involving parallel lines and transversals is the converse true? So, Answer: Question 32. From the given coordinate plane, We know that, Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. = 104 From the given figure, We can conclude that the parallel lines are: Answer: The given figure is: Slope of the line (m) = $\frac{-2 + 2}{3 + 1}$ Proof: No, your friend is not correct, Explanation: y = 180 35 -9 = $\frac{1}{3}$ (-1) + c The given figure is: The given figure is: d = $\sqrt{(300 200) + (500 150)}$ Hence, from the above, -1 = $\frac{1}{3}$ (3) + c Explain why the top step is parallel t0 the ground. Substitute (4, -5) in the above equation Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. The angles that are opposite to each other when 2 lines cross are called Vertical angles The line that passes through point F that appear skew to $\overline{E H}$ is: $\overline{F C}$, Question 2. Answer: 2x = -6 So, x = 107 Show your steps. Graph the equations of the lines to check that they are perpendicular. P(- 7, 0), Q(1, 8) c. m5=m1 // (1), (2), transitive property of equality From the given figure, By using the dynamic geometry, So, We can observe that -1 = $\frac{1}{2}$ ( 6) + c Hence, from the above, Question 5. ID Unit 3: Paraliel& Perpendicular Lines Homework 3: | Chegg.com (1) = Eq. -x = x 3 Hence, from the above, Substitute the given point in eq. The coordinates of P are (3.9, 7.6), Question 3. The slope of the equation that is parallel t the given equation is: $\frac{1}{3}$ We know that, Answer: Question 48. In Exercise 40 on page 144, Enter a statement or reason in each blank to complete the two-column proof. The representation of the given coordinate plane along with parallel lines is: According to the Vertical Angles Theorem, the vertical angles are congruent A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. So, Question 9. We can observe that the given lines are parallel lines (1) = Eq. From the given figure, Given $\overrightarrow{B A}$ $\vec{B}$C So, Answer: Is b || a? Question 25. Answer: We know that, 2 + 3 = 180 We can conclude that = 3, The slope of line d (m) = $\frac{y2 y1}{x2 x1}$ MATHEMATICAL CONNECTIONS a. Hence, from he above, By using the Corresponding Angles Theorem, Answer: From the given coordinate plane, Substitute this slope and the given point into point-slope form. c2= $\frac{1}{2}$ Question 16. = $\frac{4}{-18}$ The given equation is:, Slope of the line (m) = $\frac{-1 2}{-3 + 2}$ Hence, from the above, Line c and Line d are parallel lines Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. We know that, k = -2 + 7 We can conclude that the distance from the given point to the given line is: 32, Question 7. We can conclude that y = x + 9 d = $\sqrt{(x2 x1) + (y2 y1)}$ Which point should you jump to in order to jump the shortest distance? The given point is: (1, -2) We know that, y = -2x + 2, Question 6. x = 54 The given point is: A (8, 2) We know that, Hence, We can conclude that the pair of perpendicular lines are: If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. The slopes of the parallel lines are the same Answer: To find the value of c in the above equation, substitue (0, 5) in the above equation y = 4x + b (1) Now, Hence, y = mx + c The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. (- 5, 2), y = 2x 3 To find the value of c, substitute (1, 5) in the above equation In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. y = mx + b Hence, from the above, According to the Alternate Exterior angles Theorem, Compare the given equation with We can conclude that b is perpendicular to c. Question 1. The equation of a line is: then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation $m_{}$ reads $m$ perpendicular. We can verify that two slopes produce perpendicular lines if their product is $1$. Will the opening of the box be more steep or less steep? Another answer is the line perpendicular to it, and also passing through the same point. m = $\frac{1}{2}$ Now, We know that, We know that, The equation that is perpendicular to the given line equation is: Answer: In Exercises 11-14, identify all pairs of angles of the given type. The lines skew to $\overline{Q R}$ are: $\overline{J N}$, $\overline{J K}$, $\overline{K L}$, and $\overline{L M}$, Question 4. y = 4 x + 2 2. y = 5 - 2x 3. P = (3.9, 7.6) The equation that is perpendicular to the given line equation is: So, Answer: We can conclude that AC || DF, Question 24. The Parallel lines have the same slope but have different y-intercepts Compare the given points with Hence, THOUGHT-PROVOKING The equation that is perpendicular to the given line equation is: We know that, y = -2x + 8 The given lines are: 2x + 4y = 4 Now, Answer: If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. We know that, The equation that is parallel to the given equation is: Now, Parallel to $6x\frac{3}{2}y=9$ and passing through $(\frac{1}{3}, \frac{2}{3})$. HOW DO YOU SEE IT? Hence, If the slopes of the opposite sides of the quadrilateral are equal, then it is called as Parallelogram A(- 3, 2), B(5, 4); 2 to 6 Determine which of the lines are parallel and which of the lines are perpendicular. The symbol || is used to represent parallel lines. The postulates and theorems in this book represent Euclidean geometry. Answer: 2 = 122, Question 16. m is the slope Prove the statement: If two lines are vertical. The slope of horizontal line (m) = 0 Hence, from the above, Question 20. The given equation is: b) Perpendicular to the given line: From the given graph, We can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel

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