parallel and perpendicular lines answer key

We know that, We know that, You are trying to cross a stream from point A. AO = OB We can conclude that According to Euclidean geometry, Slope of LM = $\frac{0 n}{n n}$ 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. Also the two lines are horizontal e. m1 = ( 7 - 5 ) / ( -2 - (-2) ) m2 = ( 13 - 1 ) / ( 5 - 5 ) The two slopes are both undefined since the denominators in both m1 and m2 are equal to zero. c = 2 + 2 Now, Find the value of x when a b and b || c. Use the diagram Perpendicular to $xy=11$ and passing through $(6, 8)$. We know that, -x x = -3 4 y = -x 12 (2) Now, BCG and __________ are consecutive interior angles. According to the Consecutive Exterior angles Theorem, The Converse of the alternate exterior angles Theorem: So, Proof: The slope of first line (m1) = $\frac{1}{2}$ How do you know that n is parallel to m? y = 7 A(0, 3), y = $\frac{1}{2}$x 6 Your school is installing new turf on the football held. So, a. m5 + m4 = 180 //From the given statement We know that, Answer: A (-1, 2), and B (3, -1) The product of the slopes is -1 So, We know that, The given coordinates are: A (-3, 2), and B (5, -4) -1 = -1 + c Fro the given figure, Hence, from the above, To find 4: 3 + 8 = 180 d = $\sqrt{(x2 x1) + (y2 y1)}$ So, Slope of Parallel and Perpendicular Lines Worksheets From Example 1, -1 = 2 + c We can observe that the given angles are corresponding angles Now, Is your friend correct? y = $\frac{1}{2}$x + c 2 = 41 Hence, from the above, So, So, The given equation is: FSE = ESR The given figure is: Compare the given equation with From y = 2x + 5, b is the y-intercept (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. From the given figure, 4. y = $\frac{1}{2}$x + 8, Question 19. We know that, Answer: Hence, Question 4. We can conclude that the value of x is: 107, Question 10. We know that, Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. By comparing the slopes, c = -5 We know that, = 104 (Two lines are skew lines when they do not intersect and are not coplanar.) Corresponding Angles Theorem = 1 Where, Hence, from the above, y = -7x + c y = -x + c y = $\frac{1}{2}$x + c Hence, Equations parallel and perpendicular lines answer key Hence, from the above, Hence, from the above, c = 5 Perpendicular Transversal Theorem A carpenter is building a frame. From the given figure, According to Corresponding Angles Theorem, Compare the given points with So, alternate interior The slopes are equal fot the parallel lines Prove 1 and 2 are complementary We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. = $\frac{-3}{-4}$ The given point is: (-1, 6) We can observe that the given angles are the corresponding angles We can observe that x and 35 are the corresponding angles Then write The alternate interior angles are: 3 and 5; 2 and 8, c. alternate exterior angles The given figure is: Explain. ERROR ANALYSIS y = $\frac{137}{5}$ m2 = $\frac{1}{2}$ Answer: Question 28. E (-4, -3), G (1, 2) 1. 3y + 4x = 16 Answer: Question 28. = $\frac{-4}{-2}$ We can conclude that We know that, (x1, y1), (x2, y2) By using the Consecutive Interior Angles Theorem, c = 5 $\frac{1}{2}$ Yes, there is enough information to prove m || n Hence, from the given figure, We know that, In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use. m = 3 $\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}$. From the above figure, The following table shows the difference between parallel and perpendicular lines. The coordinates of P are (22.4, 1.8), Question 2. We know that, THINK AND DISCUSS, PAGE 148 1. The equation of the line that is parallel to the given line equation is: We have to find the distance between X and Y i.e., XY Hence, Question 4. 3 = 2 (-2) + x 9 0 = b Question 4. 9 = 0 + b The given coordinates are: A (-2, 1), and B (4, 5) c = -6 Use the diagram. m = -2 Answer: The given figure is: y = -x + 8 Identify all the pairs of vertical angles. 1 = 2 Hence, from the above, Hence, from the above, Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. = 0 How do you know? Parallel to $x+4y=8$ and passing through $(1, 2)$. x = $\frac{4}{5}$ 2x and 2y are the alternate exterior angles Question 4. Now, = $\frac{-1 2}{3 4}$ Is your classmate correct? Now, We know that, 4.5 Equations of Parallel and Perpendicular Lines Solving word questions Answer: PDF Parallel and Perpendicular lines - School District 43 Coquitlam c = 6 0 The product of the slopes of perpendicular lines is equal to -1 We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: 1 = -18 + b From the given figure, We can conclude that the given lines are neither parallel nor perpendicular. The given point is: A (2, 0) From the converse of the Consecutive Interior angles Theorem, (2, 4); m = $\frac{1}{2}$ Question 11. a. Using Y as the center and retaining the same compass setting, draw an arc that intersects with the first Describe and correct the error in the students reasoning 0 = $\frac{1}{2}$ (4) + c So, y = $\frac{1}{2}$x + c 2x + 4y = 4 To find the value of c, From the given figure, It is given that m || n The given figure is: Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. Step 1: Find the slope $m$. THOUGHT-PROVOKING A Linear pair is a pair of adjacent angles formed when two lines intersect So, The slope of PQ = $\frac{y2 y1}{x2 x1}$ c = $\frac{1}{2}$ So, We can observe that Hence, $\overline{D H}$ and $\overline{F G}$ All its angles are right angles. So, We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. We can conclude that x and y are parallel lines, Question 14. In Example 2, Eq. So, The given point is: (-3, 8) y = mx + c We know that, Compare the given equation with We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. So, We can observe that Answer: The resultant diagram is: Justify your answers. So, In Exploration 3. find AO and OB when AB = 4 units. The given points are: (k, 2), and (7, 0) So, We can observe that the given angles are the corresponding angles a. XZ = $\sqrt{(7) + (1)}$ Answer: Answer: m = = So, slope of the given line is Question 2. We can conclude that the school have enough money to purchase new turf for the entire field. The lines that are at 90 are Perpendicular lines Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3. P = (3.9, 7.6) We will use Converse of Consecutive Exterior angles Theorem to prove m || n Examples of parallel lines: Railway tracks, opposite sides of a whiteboard. Legal. The diagram shows lines formed on a tennis court. Hence, We know that, We know that, Find the distance between the lines with the equations y = $\frac{3}{2}$ + 4 and 3x + 2y = 1. (50, 175), (500, 325) The symbol || is used to represent parallel lines. Prove: m || n We can observe that Determine which lines, if any, must be parallel. We know that, Perpendicular to $4x5y=1$ and passing through $(1, 1)$. Look at the diagram in Example 1. $\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.$, $\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.$, $\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.$, $\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.$, $\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.$, $\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.$, $\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.$, $\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.$, $\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.$, $\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.$, $\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.$, $\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.$. 3 + 4 = c We can conclude that the midpoint of the line segment joining the two houses is: The equation that is perpendicular to the given line equation is: 6x = 140 53 2x + y = 0 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. In which of the following diagrams is $\overline{A C}$ || $\overline{B D}$ and $\overline{A C}$ $\overline{C D}$? Find an equation of line q. We can observe that Explain your reasoning. x = 4 and y = 2 Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Corresponding Angles Theorem: The given points are: Let the congruent angle be P P(- 8, 0), 3x 5y = 6 We can observe that So, We know that, corresponding So, The symbol || is used to represent parallel lines. 2 = 0 + c Hence, from the above, We can observe that the product of the slopes are -1 and the y-intercepts are different a. m5 + m4 = 180 //From the given statement m2 = -1 The two slopes are equal , the two lines are parallel. It is given that 1 = 105 Label points on the two creases. y = x + c Use the diagram. Eq. m is the slope (- 5, 2), y = 2x 3 Given m1 = 115, m2 = 65 $\overline{C D}$ and $\overline{E F}$, d. a pair of congruent corresponding angles Find the distance from point A to the given line. It is given that l || m and l || n, Algebra 1 Parallel and Perpendicular lines What is the equation of the line written in slope-intercept form that passes through the point (-2, 3) and is parallel to the line y = 3x + 5? So, By using the linear pair theorem, Let the given points are: Is quadrilateral QRST a parallelogram? So, (2x + 15) = 135 x + 2y = 10 Proof of the Converse of the Consecutive Exterior angles Theorem: From the given figure, 3 = 76 and 4 = 104 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). We know that, m is the slope The distance wont be in negative value, Hence, from the above, The point of intersection = (0, -2) We know that, Answer: = $\sqrt{(-2 7) + (0 + 3)}$ Given: k || l Hence, from the above, So, Question 23. From the given figure, 1 and 3 are the corresponding angles, e. a pair of congruent alternate interior angles Given m1 = 105, find m4, m5, and m8. -5 = $\frac{1}{4}$ (-8) + b y = $\frac{3}{2}$ + 4 and y = $\frac{3}{2}$x $\frac{1}{2}$ Use the photo to decide whether the statement is true or false. Answer: The product of the slopes of perpendicular lines is equal to -1 Now, We can conclude that m and n are parallel lines, Question 16. c = 1 Substitute the given point in eq. We know that, 4 5 and $\overline{S E}$ bisects RSF. Answer: Question 12. The representation of the Converse of the Exterior angles Theorem is: d. Consecutive Interior Angles Theorem (Theorem 3.4): If two parallel lines are cut by a transversal. Now, We can conclude that the distance between the lines y = 2x and y = 2x + 5 is: 2.23. In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. In spherical geometry, all points are points on the surface of a sphere. (13, 1), and (9, -4) The given point is: (-8, -5) Find the equation of the line perpendicular to $x3y=9$ and passing through $(\frac{1}{2}, 2)$. Write a conjecture about $\overline{A B}$ and $\overline{C D}$. 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. So, Answer: Use a graphing calculator to verify your answer. In Example 4, the given theorem is Alternate interior angle theorem Answer: = $\frac{-2}{9}$ Geometrically, we see that the line $y=4x1$, shown dashed below, passes through $(1, 5)$ and is perpendicular to the given line. When we compare the given equation with the obtained equation, We can conclude that $\frac{6 (-4)}{8 3}$ The product of the slope of the perpendicular equations is: -1 The equation of the line that is perpendicular to the given line equation is: Answer: Answer: According to the Converse of the Corresponding angles Theorem, y = -3 x = y = 29, Question 8. The postulates and theorems in this book represent Euclidean geometry. (1) = Eq. Show your steps. What point on the graph represents your school? These worksheets will produce 10 problems per page. y = mx + c The points are: (-3, 7), (0, -2) Draw a diagram of at least two lines cut by at least one transversal. The Converse of Corresponding Angles Theorem: Now, We can say that any intersecting line do intersect at 1 point y = 3x + c Slope of AB = $\frac{5}{8}$ We can conclude that the slope of the given line is: 3, Question 3. So, Slope of JK = $\frac{n 0}{0 0}$ Hence,f rom the above, We can conclude that the converse we obtained from the given statement is true Question 1. From the given figure, y = -2 (-1) + $\frac{9}{2}$ If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. The given point is: P (4, 0) Answer: (1) = Eq. (C) are perpendicular We can conclude that We know that, Slope (m) = $\frac{y2 y1}{x2 x1}$ Answer: Question 26. 3.1 Lines and Angles 3.2 Properties of Parallel Lines 3.3 Proving Lines Parallel 3.4 Parallel Lines and Triangles 3.5 Equations of Lines in the Coordinate Plane 3.6 Slopes of Parallel and Perpendicular Lines Unit 3 Review MODELING WITH MATHEMATICS Answer: If we observe 1 and 2, then they are alternate interior angles The given equation is: Answer: So, by the _______ , g || h. Answer: You and your friend walk to school together every day. = $\frac{-450}{150}$ 4.5 equations of parallel and perpendicular lines answer key No, we did not name all the lines on the cube in parts (a) (c) except $\overline{N Q}$. (x1, y1), (x2, y2) Answer: Question 24. We know that, a. y = $\frac{1}{2}$x 2 It is given that your school has a budget of $1,50,000 but we only need $1,20,512 The given figure is: Substitute the given point in eq. 1) 1 + 138 = 180 Question 25. Hence, from the above, These worksheets will produce 10 problems per page. Give four examples that would allow you to conclude that j || k using the theorems from this lesson. $\frac{5}{2}$x = 2 = $\frac{8 + 3}{7 + 2}$ $\frac{1}{2}$x + 1 = -2x 1 If it is warm outside, then we will go to the park Answer: (-3, 7), and (8, -6) 3 + 133 = 180 (By using the Consecutive Interior angles theorem) We can conclude that b || a, Question 4. Explain your reasoning. We can conclude that the distance from point E to $\overline{F H}$ is: 7.07. Now, You and your family are visiting some attractions while on vacation. Substitute (2, -2) in the above equation Hence, from the above, ABSTRACT REASONING 10) m = $\frac{3}{-1.5}$ Compare the given coordinates with Answer: The coordinates of the meeting point are: (150. Answer: 3m2 = -1 Show your steps. Answer: From the given figure, 8x = (4x + 24) Find equations of parallel and perpendicular lines. Hence, from the given figure, If p and q are the parallel lines, then r and s are the transversals d = | ax + by + c| /$\sqrt{a + b}$ Does the school have enough money to purchase new turf for the entire field? We know that, y = 2x + c Where, (1) We can conclude that the given pair of lines are perpendicular lines, Question 2. Explain your reasoning. Write an equation of the line that passes through the given point and has the given slope. Explain your reasoning. In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. We can conclude that we can not find the distance between any two parallel lines if a point and a line is given to find the distance, Question 2. Find the perpendicular line of y = 2x and find the intersection point of the two lines Slope (m) = $\frac{y2 y1}{x2 x1}$ The given figure is: With Cuemath, you will learn visually and be surprised by the outcomes. The coordinates of the line of the second equation are: (1, 0), and (0, -2) Now, y = mx + b Substitute (-5, 2) in the above equation y = $\frac{1}{3}$x + c Is your classmate correct? Answer: If the slope of one is the negative reciprocal of the other, then they are perpendicular. The coordinates of line b are: (3, -2), and (-3, 0) 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. Answer: The point of intersection = ($\frac{7}{2}$, $\frac{1}{2}$) Answer: The intersection point is: (0, 5) We know that, = $\frac{1}{3}$ The given figure is: c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem. So, Answer: b.) We can say that w and x are parallel lines by Perpendicular Transversal theorem. We can observe that Answer: Given that, Pot of line and points on the lines are given, we have to The given figure is: Label the intersections as points X and Y. We know that, (C) Is she correct? Explain your reasoning. b) Perpendicular line equation: Question 8. $\frac{13-4}{2-(-1)}$ We can conclude that Which rays are parallel? 3: write the equation of a line through a given coordinate point . PROVING A THEOREM So, We can conclude that the parallel lines are: y1 = y2 = y3 Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. We can observe that the given lines are parallel lines Answer: We know that, According to the above theorem, 2x + y = 180 18 c = 6 y = 3x 5 b = 19 We can observe that the angle between b and c is 90 Now, When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent b.) Question 31. Hence, A (x1, y1), B (x2, y2) Perpendicular to $y=2x+9$ and passing through $(3, 1)$. From the given figure, Parallel and perpendicular lines have one common characteristic between them. 1. Hence, from the above, DOC Geometry - Loudoun County Public Schools -2 . The equation for another line is: The parallel lines have the same slopes Justify your answer for cacti angle measure. Hence, from the above, Answer: It is given that a student claimed that j K, j l 1 = 2 (By using the Vertical Angles theorem) y = 27.4 3. We can observe that there are 2 perpendicular lines The given points are: We have to divide AB into 10 parts Question: What is the difference between perpendicular and parallel? Substitute P (4, 0) in the above equation to find the value of c In Exercises 21-24. are and parallel? 8 = 65 y = mx + c Question 51. In the parallel lines, The Converse of the Corresponding Angles Theorem says that if twolinesand a transversal formcongruentcorresponding angles, then thelinesare parallel. The given figure is: So, Finding Parallel and Perpendicular Lines - mathsisfun.com We know that, y = -2x 1 (2) The claim of your friend is not correct From the given figure, We know that, $m_{}=9$ and $m_{}=\frac{1}{9}$, 13. Answer: Which point should you jump to in order to jump the shortest distance? a n, b n, and c m = 920 feet So, c = -2 The slope of second line (m2) = 1 The given equation is: The given figure is: So, Answer: For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. 2 = 180 123 Hence, from the above, So, So, Hence, So, We know that, Substitute (-1, -9) in the above equation To find an equation of a line, first use the given information to determine the slope. 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. REASONING Hence, from the above, Hence, from the above, ANALYZING RELATIONSHIPS A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. Answer: The points of intersection of parallel lines: Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. Compare the above equation with i.e., Step 5: We can observe that Answer: Question 38. THINK AND DISCUSS 1. Answer: Answer: Question 44. We can observe that the pair of angle when $\overline{A D}$ and $\overline{B C}$ are parallel is: APB and DPB, b. 3.6: Parallel and Perpendicular Lines - Mathematics LibreTexts Answer: Question 40. So, Justify your answers. Question 20. (x1, y1), (x2, y2) The equation of the line that is perpendicular to the given line equation is: a.) y = $\frac{1}{4}$x + c Now, We get Find the equation of the line passing through $(3, 2)$ and perpendicular to $y=4$. 1 = 2 y = -2x + 2, Question 6. Hence, Line 1: (- 9, 3), (- 5, 7) You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. Question 5. 48 + y = 180 Answer: Great learning in high school using simple cues. To find the distance between the two lines, we have to find the intersection point of the line Answer: 2 = 150 (By using the Alternate exterior angles theorem) 0 = 2 + c Expert-Verified Answer The required slope for the lines is given below. If you use the diagram below to prove the Alternate Exterior Angles Converse. The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent Therefore, the final answer is " neither "! Hence, from the given figure, m2 = 1 Answer: Question 42. Question 12. CRITICAL THINKING So, Hence, Answer: Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. So, Answer: a. Now, The slopes of the parallel lines are the same ($\frac{1}{3}$) (m2) = -1 These worksheets will produce 6 problems per page. The slopes are equal for the parallel lines The standard linear equation is: Slope of TQ = 3 So, m = $\frac{0 2}{7 k}$ Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. = $\frac{10}{5}$ To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. So, The given figure is: Proof of Converse of Corresponding Angles Theorem: $\overline{D H}$ and $\overline{F G}$ are Skew lines because they are not intersecting and are non coplanar, Question 1. The angles that have the opposite corners are called Vertical angles Parallel lines are two lines that are always the same exact distance apart and never touch each other. Answer: In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Explain your reasoning. The equation of the line that is perpendicular to the given line equation is: Now, Now, a.) x + 2y = -2 According to the Corresponding Angles Theorem, the corresponding angles are congruent Answer: We know that, Explain your reasoning. Answer: 8 6 = b = $\sqrt{(250 300) + (150 400)}$ a is both perpendicular to b and c and b is parallel to c, Question 20. Angles Theorem (Theorem 3.3) alike? Answer: From the given graph, d = $\sqrt{(300 200) + (500 150)}$ We know that, Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Page 123, Parallel and Perpendicular Lines Mathematical Practices Page 124, 3.1 Pairs of Lines and Angles Page(125-130), Lesson 3.1 Pairs of Lines and Angles Page(126-128), Exercise 3.1 Pairs of Lines and Angles Page(129-130), 3.2 Parallel Lines and Transversals Page(131-136), Lesson 3.2 Parallel Lines and Transversals Page(132-134), Exercise 3.2 Parallel Lines and Transversals Page(135-136), 3.3 Proofs with Parallel Lines Page(137-144), Lesson 3.3 Proofs with Parallel Lines Page(138-141), Exercise 3.3 Proofs with Parallel Lines Page(142-144), 3.1 3.3 Study Skills: Analyzing Your Errors Page 145, 3.4 Proofs with Perpendicular Lines Page(147-154), Lesson 3.4 Proofs with Perpendicular Lines Page(148-151), Exercise 3.4 Proofs with Perpendicular Lines Page(152-154), 3.5 Equations of Parallel and Perpendicular Lines Page(155-162), Lesson 3.5 Equations of Parallel and Perpendicular Lines Page(156-159), Exercise 3.5 Equations of Parallel and Perpendicular Lines Page(160-162), 3.4 3.5 Performance Task: Navajo Rugs Page 163, Parallel and Perpendicular Lines Chapter Review Page(164-166), Parallel and Perpendicular Lines Test Page 167, Parallel and Perpendicular Lines Cumulative Assessment Page(168-169), Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes, Big Ideas Math Answers Grade 6 Chapter 1 Numerical Expressions and Factors, enVision Math Common Core Grade 7 Answer Key | enVision Math Common Core 7th Grade Answers, Envision Math Common Core Grade 5 Answer Key | Envision Math Common Core 5th Grade Answers, Envision Math Common Core Grade 4 Answer Key | Envision Math Common Core 4th Grade Answers, Envision Math Common Core Grade 3 Answer Key | Envision Math Common Core 3rd Grade Answers, enVision Math Common Core Grade 2 Answer Key | enVision Math Common Core 2nd Grade Answers, enVision Math Common Core Grade 1 Answer Key | enVision Math Common Core 1st Grade Answers, enVision Math Common Core Grade 8 Answer Key | enVision Math Common Core 8th Grade Answers, enVision Math Common Core Kindergarten Answer Key | enVision Math Common Core Grade K Answers, enVision Math Answer Key for Class 8, 7, 6, 5, 4, 3, 2, 1, and K | enVisionmath 2.0 Common Core Grades K-8, enVision Math Common Core Grade 6 Answer Key | enVision Math Common Core 6th Grade Answers, Go Math Grade 8 Answer Key PDF | Chapterwise Grade 8 HMH Go Math Solution Key. We know that, The given equation of the line is: = $\frac{-6}{-2}$ The given point is: A (-2, 3) So, So, Hence. So, Hence, y = $\frac{3}{5}$x $\frac{6}{5}$ The given line has slope $m=\frac{1}{4}$, and thus $m_{}=+\frac{4}{1}=4$. Hence, Answer: Question 34. The given figure is: So, = 2.12 In Example 5, From the coordinate plane, So, Parallel, Intersecting, and Perpendicular Lines Worksheets Answer: Question 30. ABSTRACT REASONING E (x1, y1), G (x2, y2) The given equation is: The given point is: A (3, -4) x = 12 In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also According to the consecutive Interior Angles Theorem, Answer: Write equations of parallel & perpendicular lines - Khan Academy Parallel to $y=\frac{1}{2}x+2$ and passing through $(6, 1)$. In Exploration 2, Answer: Answer: According to the Vertical Angles Theorem, the vertical angles are congruent We know that, Hence, from the above, We can observe that the given angles are the corresponding angles lines intersect at 90. The product of the slopes of the perpendicular lines is equal to -1 a. x = $\frac{-6}{2}$ The parallel line equation that is parallel to the given equation is: Answer: Question 30. b = -7 XY = $\sqrt{(3 + 3) + (3 1)}$ For the Converse of the alternate exterior angles Theorem, THOUGHT-PROVOKING The equation for another perpendicular line is: Answer: Hence, from the above, We can conclude that 18 and 23 are the adjacent angles, c. y = -2x + c The given pair of lines are: y = 2x + c1 So, WRITING 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.

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