parallel and perpendicular lines answer key

If a || b and b || c, then a || c So, (a) parallel to the line y = 3x 5 and Hence, from the above, We know that, Hence, from the above, 1 = 2 (By using the Vertical Angles theorem) $m_{}=\frac{4}{3}$ and $m_{}=\frac{3}{4}$, 15. XY = $\sqrt{(3 + 3) + (3 1)}$ So, Answer: We can conclude that the value of x is: 14. From the figure, y = mx + b We know that, We can conclude that m || n, Question 15. 15) through: (4, -1), parallel to y = - 3 4 x16) through: (4, 5), parallel to y = 1 4 x - 4 17) through: (-2, -5), parallel to y = x + 318) through: (4, -4), parallel to y = 3 19) through . So, y = x + 4 Answer: Question 18. alternate exterior Slope of the line (m) = $\frac{y2 y1}{x2 x1}$ We can conclude that Another answer is the line perpendicular to it, and also passing through the same point. (- 8, 5); m = $\frac{1}{4}$ 1 = 123 Answer: From the above, Hence, from the above, y = 7 Lets draw that line, and call it P. Lets also call the angle formed by the traversal line and this new line angle 3, and we see that if we add some other angle, call it angle 4, to it, it will be the same as angle 2. -4 1 = b Compare the given points with (x1, y1), and (x2, y2) By comparing eq. = $\frac{-6}{-2}$ b. Which line(s) or plane(s) appear to fit the description? Answer: We know that, The given figure is: XY = $\sqrt{(3 + 3) + (3 1)}$ = $\sqrt{(3 / 2) + (3 / 2)}$ The given line has the slope $m=\frac{1}{7}$, and so $m_{}=\frac{1}{7}$. In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use. From the given bars, $\overline{I J}$ and $\overline{C D}$, c. a pair of paralIeI lines y = -x + c CONSTRUCTION Slope (m) = $\frac{y2 y1}{x2 x1}$ 42 and (8x + 2) are the vertical angles Hence, from the above, For parallel lines, we cant say anything y = 2x + c2, b. 1 = 40 2x y = 4 Draw $\overline{P Z}$, CONSTRUCTION your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. y = $\frac{156}{12}$ y = mx + b We can conclude that both converses are the same The equation that is perpendicular to the given line equation is: When you look at perpendicular lines they have a slope that are negative reciprocals of each other. x = 97, Question 7. HOW DO YOU SEE IT? The equation of the line that is parallel to the given equation is: $m_{}=\frac{3}{2}$ and $m_{}=\frac{2}{3}$, 19. XZ = $\sqrt{(7) + (1)}$ The given points are: Answer: m2 = $\frac{1}{3}$ Hence, In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. Answer: The equation that is perpendicular to the given line equation is: The product of the slopes of perpendicular lines is equal to -1 Answer: We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. Given a||b, 2 3 Answer: Question 16. The given figure is: Given: k || l, t k So, From the given graph, Which lines intersect ? By using the Corresponding Angles Theorem, So, If we try to find the slope of a perpendicular line by finding the opposite reciprocal, we run into a problem: $m_{}=\frac{1}{0}$, which is undefined. Hence, from the above, y y1 = m (x x1) Now, We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. Which values of a and b will ensure that the sides of the finished frame are parallel.? So, Question 20. 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. Hence, from the above, (1) y = $\frac{3}{2}$ x = 14.5 The parallel lines have the same slopes 2x + y = 180 18 We can conclude that Therefore, they are parallel lines. The product of the slopes of the perpendicular lines is equal to -1 The equation that is parallel to the given equation is: Answer: Hence, from the above, b is the y-intercept (1) = Eq. c = 2 = $1,20,512 Slope of RS = $\frac{-3}{-1}$ $m\cdot m_{\perp}=-\frac{5}{8}\cdot\frac{8}{5}=-\frac{40}{40}=-1\quad\color{Cerulean}{\checkmark}$. To find the distance from line l to point X, The equation for another line is: : n; same-side int. m1 = $\frac{1}{2}$, b1 = 1 P(- 7, 0), Q(1, 8) The given figure is: Question 18. Write an inequality for the slope of a line perpendicular to l. Explain your reasoning. Lines Perpendicular to a Transversal Theorem (Thm. y = -2x + c M = (150, 250), b. -9 = $\frac{1}{3}$ (-1) + c Answer: Now, 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. So, COMPLETE THE SENTENCE P(0, 0), y = 9x 1 Answer: Compare the given equation with line(s) perpendicular to 6 + 4 = 180, Question 9. X (-3, 3), Y (3, 1) Answer: Prove the statement: If two lines are vertical. THINK AND DISCUSS, PAGE 148 1. So, Now, The parallel lines have the same slopes Hence, (50, 175), (500, 325) y = $\frac{1}{3}$x + c $\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.$, $\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.$, $\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.$, $\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.$, $\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.$, $\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.$, $\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.$, $\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.$, $\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.$, $\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.$, $\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.$, $\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.$. It is given that, Hence, from the above, -1 = $\frac{1}{2}$ ( 6) + c y = -2x + 8 The given equation is: Slope of QR = $\frac{1}{2}$, Slope of RS = $\frac{1 4}{5 6}$ Remember that horizontal lines are perpendicular to vertical lines. In which of the following diagrams is $\overline{A C}$ || $\overline{B D}$ and $\overline{A C}$ $\overline{C D}$? d = | 2x + y | / $\sqrt{5}$} We can observe that HOW DO YOU SEE IT? a. We know that, Answer: x = 147 14 4x y = 1 Is your classmate correct? From the given figure, = $\frac{2}{9}$ = $\frac{11}{9}$ c = -4 + 3 Hence, from the above, Hence, from the above, x = 2 m1 m2 = -1 The rope is pulled taut. Now, The coordinates of line q are: From the figure, We can conclude that Verify your formula using a point and a line. Answer: The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. From the given figure, m = $\frac{1}{6}$ and c = -8 1 = 42 Answer: c = -2 Answer: Identify all pairs of angles of the given type. We can conclude that Answer: The given figure is: The equation that is perpendicular to the given equation is: We can conclude that p and q; r and s are the pairs of parallel lines. We can say that any parallel line do not intersect at any point So, Hence, The completed table is: Question 1. Hence, Hence, from the above, We can conclude that it is not possible that a transversal intersects two parallel lines. XY = $\sqrt{(x2 x1) + (y2 y1)}$ We can conclude that the pair of perpendicular lines are: From the given figure, We can conclude that The given figure is: lines intersect at 90. The given equation is:, (7x 11) = (4x + 58) Explain why the top rung is parallel to the bottom rung. Now, Now, You are looking : parallel and perpendicular lines maze answer key pdf Contents 1. THOUGHT-PROVOKING In Exercise 40 on page 144. explain how you started solving the problem and why you started that way. Hence, Now, = $\sqrt{(-2 7) + (0 + 3)}$ Therefore, the final answer is " neither "! x + 2y = 10 Substitute the given point in eq. The letter A has a set of perpendicular lines. Answer: Prove: t l x + 2y = 2 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 Answer: Hence, from the above, To find the value of c, m = $\frac{3}{1.5}$ It is given that Now, So, = 4 Answer: y = -3x + b (1) Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. x = y = 29, Question 8. In Exercises 13 and 14, prove the theorem. The coordinates of x are the same. Hence, Question 13. Sandwich: The highlighted lines in the sandwich are neither parallel nor perpendicular lines. plane(s) parallel to plane CDH We can observe that there is no intersection between any bars From the given coordinate plane, Compare the given equation with Where, According to Euclidean geometry, We can observe that, From the given figure, Answer: Question 26. We know that, Answer: For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts We can say that all the angle measures are equal in Exploration 1 We were asked to find the equation of a line parallel to another line passing through a certain point. Hence, from the above, The coordinates of the school = (400, 300) Hence, from the given figure, Hence, c = -2 Question 13. We know that, Determine which lines, if any, must be parallel. 4.5 Equations of Parallel and Perpendicular Lines Solving word questions Hence, from the above figure, y = $\frac{1}{2}$x 3, b. Construct a square of side length AB In spherical geometry. 4 5, b. c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. Hence, from the above, Question 23. if two lines are perpendicular to the same line. Answer: Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Write an equation of a line parallel to y = x + 3 through (5, 3) Q. The given figure is: = 180 76 We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. Measure the lengths of the midpoint of AB i.e., AD and DB. Answer: From the given figure, In this case, the slope is $m_{}=\frac{1}{2}$ and the given point is $(8, 2)$. We can conclude that we can use Perpendicular Postulate to show that $\overline{A C}$ is not perpendicular to $\overline{B F}$, Question 3. We know that, The vertical angles are: 1 and 3; 2 and 4 y = $\frac{1}{4}$x + c 3 + 4 = c y = $\frac{137}{5}$ d = $\frac{4}{5}$ Find m2 and m3. We can observe that Explain your reasoning. Simply click on the below available and learn the respective topics in no time. 0 = 3 (2) + c Hence, Answer: Question 40. Will the opening of the box be more steep or less steep? 0 = $\frac{5}{3}$ ( -8) + c k = -2 + 7 The given figure is: The given point is: A (-9, -3) Are the numbered streets parallel to one another? 1 = 32. 1 = 4 5y = 3x 6 b = 9 Substitute (-5, 2) in the above equation USING STRUCTURE According to the above theorem, We can observe that the given lines are parallel lines Question 27. Alternate Exterior Angles Converse (Theorem 3.7) The slope of the parallel equations are the same We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Substitute (1, -2) in the above equation MODELING WITH MATHEMATICS Slope (m) = $\frac{y2 y1}{x2 x1}$ y = -2x 2 x + x = -12 + 6 So, -x + 2y = 12 Label the ends of the crease as A and B. Question 7. The slope of the given line is: m = 4 Question 5. Prove 1 and 2 are complementary Hence, from the above, Which theorems allow you to conclude that m || n? Perpendicular transversal theorem: We can conclude that option D) is correct because parallel and perpendicular lines have to be lie in the same plane, Question 8. The vertical angles are congruent i.e., the angle measures of the vertical angles are equal So, The equation that is parallel to the given equation is: So, The slopes are the same and the y-intercepts are different The slope of line a (m) = $\frac{y2 y1}{x2 x1}$ Answer: Question 28. 8 = 180 115 The given equation is: Now, So, We can observe that there are a total of 5 lines. The opposite sides of a rectangle are parallel lines. When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90, Work with a partner. From the given figure, m2 = 2 Question 1. USING STRUCTURE The sum of the given angle measures is: 180 Answer: Answer: Question 20. y = $\frac{1}{3}$ (10) 4 Hence, from the above, So, Now, Explain your reasoning. Compare the given points with (x1, y1), and (x2, y2) Which pair of angle measures does not belong with the other three? So, The conjecture about $\overline{A B}$ and $\overline{c D}$ is: Identify two pairs of parallel lines so that each pair is in a different plane. The given figure is: Hence, from the above, y = -3 (0) 2 AB = 4 units Parallel lines are lines in the same plane that never intersect. We can observe that the given angles are consecutive exterior angles 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. Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. The points of intersection of intersecting lines: Select the orange Get Form button to start editing. Question 31. Answer: Question 2. From the figure, The representation of the given point in the coordinate plane is: Question 54. We can observe that 2x y = 18 (5y 21) ad (6x + 32) are the alternate interior angles A(- 3, 7), y = $\frac{1}{3}$x 2 So, The sides of the angled support are parallel. REASONING If we observe 1 and 2, then they are alternate interior angles y = -x -(1) So, The given rectangular prism of Exploration 2 is: The given figure is: = 2, The slope of line c (m) = $\frac{y2 y1}{x2 x1}$ Question 45. y = mx + c Hene, from the given options, The mathematical notation $m_{}$ reads $m$ parallel.. From ESR, So, Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 A student says. Line 2: (7, 0), (3, 6) Answer: a n, b n, and c m We know that, Question 41. 3m2 = -1 Perpendicular lines are lines in the same plane that intersect at right angles ($90$ degrees). (x1, y1), (x2, y2) Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line. Write the converse of the conditional statement. Answer: Line c and Line d are parallel lines Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. (-1) (m2) = -1 The slope of the line of the first equation is: 2x = 18 Answer: We can conclude that -4 = -3 + c Make a conjecture about how to find the coordinates of a point that lies beyond point B along $\vec{A}$B. These guidelines, with the editor will assist you with the whole process. $\frac{6 (-4)}{8 3}$ Draw a diagram of at least two lines cut by at least one transversal. m1 m2 = -1 These worksheets will produce 6 problems per page. The given lines are the parallel lines Explain why the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem (Theorem 3.1). We know that, Explain Your reasoning. y = $\frac{8}{5}$ 1 a. Hence, from the above, 6x = 87 The perpendicular lines have the product of slopes equal to -1 Line 1: (- 3, 1), (- 7, 2) The two lines are vertical lines and therefore parallel. We can observe that not any step is intersecting at each other a. Find the slope of the line perpendicular to $15x+5y=20$. Bertha Dr. is parallel to Charles St. From the given figure, It is given that a student claimed that j K, j l Here the given line has slope $m=\frac{1}{2}$, and the slope of a line parallel is $m_{}=\frac{1}{2}$. Parallel to $2x3y=6$ and passing through $(6, 2)$. To find the coordinates of P, add slope to AP and PB The slopes are equal fot the parallel lines Hence, from the above, Statement of consecutive Interior angles theorem: We know that, Question 47. The perpendicular equation of y = 2x is: Answer: Question 2. Hence, from the above, In the diagram below. Now, Draw an arc with center A on each side of AB. $\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}$. we know that, Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals. Explain your reasoning. y = $\frac{77}{11}$ When the corresponding angles are congruent, the two parallel lines are cut by a transversal y = mx + c We can conclude that the distance from point A to the given line is: 2.12, Question 26. x = -3 The points are: (0, 5), and (2, 4) Find the perpendicular line of y = 2x and find the intersection point of the two lines Question 3. Compare the given points with The parallel line equation that is parallel to the given equation is: Compare the given equation with Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. ax + by + c = 0 The given point is: (3, 4) The angles that are opposite to each other when two lines cross are called Vertical angles Proof: Answer: The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines In Exercises 43 and 44, find a value for k based on the given description. 8 = 105, Question 2. = (4, -3) = $\frac{6 + 4}{8 3}$ = 5.70 = $\frac{15}{45}$ Question 21. $\begin{array}{cc} {\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(-1,-5)}&{m_{\perp}=4}\end{array}$. 2 and7 3 = 60 (Since 4 5 and the triangle is not a right triangle) We can say that any coincident line do not intersect at any point or intersect at 1 point The slope of horizontal line (m) = 0 (y + 7) = (3y 17) We have seen that the graph of a line is completely determined by two points or one point and its slope. It can be observed that All its angles are right angles. y = mx + c Hence, from the above, $\overline{A B}$ and $\overline{G H}$, b. a pair of perpendicular lines (B) Alternate Interior Angles Converse (Thm 3.6) Question 22. justify your answer. We can observe that 1 (m2) = -3 Horizontal and vertical lines are perpendicular to each other. Then, let's go back and fill in the theorems. Question 38. We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. 1 and 3 are the vertical angles The given points are: (k, 2), and (7, 0) The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. The given point is: (-1, -9) Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) We can conclude that the quadrilateral QRST is a parallelogram. The product of the slopes of the perpendicular lines is equal to -1 The following summaries about parallel and perpendicular lines maze answer key pdf will help you make more personal choices about more accurate and faster information. d = $\sqrt{(x2 x1) + (y2 y1)}$ x 6 = -x 12 Converse: ABSTRACT REASONING y = 162 18 We know that, 132 = (5x 17) = 2, The slope of line b (m) = $\frac{y2 y1}{x2 x1}$ y = $\frac{1}{4}$x 7, Question 9. x y = -4 m = 2 Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. From the figure, Lines AB and CD are not intersecting at any point and are always the same distance apart. The given equation is: It is not always the case that the given line is in slope-intercept form. We know that, According to the Alternate Exterior angles Theorem, Parallel & Perpendicular Lines Practice Answer Key Parallel and Perpendicular Lines Key *Note:If Google Docs displays "Sorry, we were unable to retrieve the document for viewing," refresh your browser. Now, So, In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. Hence, from the above, Now, We can conclude that the given statement is not correct. c = 2 0 = $\sqrt{(3 / 2) + (3 / 4)}$ So, Question 22. y = 2x + 12 In the equation form of a line y = mx +b lines that are parallel will have the same value for m. Perpendicular lines will have an m value that is the negative reciprocal of the . Perpendicular to $x=\frac{1}{5}$ and passing through $(5, 3)$. First, find the slope of the given line. When two lines are crossed by another line (which is called the Transversal), theangles in matching corners are called Corresponding angles The standard form of the equation is: In Exercises 11-14, identify all pairs of angles of the given type. The given figure is: From the above figure, 4 = 105, To find 5: Hence, m1 and m5 These lines can be identified as parallel lines. m = $\frac{3}{-1.5}$ Now, 9 = 0 + b Answer: Answer: m is the slope a. Which theorem is the student trying to use? So, Substitute A (-6, 5) in the above equation to find the value of c So, y = -2x + 3 0 = 2 + c Hence, Perpendicular to $y=2x+9$ and passing through $(3, 1)$. Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3). 0 = $\frac{1}{2}$ (4) + c For a horizontal line, They are always equidistant from each other. So, Answer: Hence, from the above, a. m5 + m4 = 180 //From the given statement Slope (m) = $\frac{y2 y1}{x2 x1}$ Slope of line 1 = $\frac{9 5}{-8 10}$ y = -9 From the given figure, Answer: Question 32. MAKING AN ARGUMENT x + 73 = 180 Hence, from the above, Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent 1 and 5 are the alternate exterior angles m2 = -2 Use the Distance Formula to find the distance between the two points.