parallel and perpendicular lines answer key

The lines perpendicular to $\overline{E F}$ are: $\overline{F B}$ and $\overline{F G}$, Question 3. The equation that is parallel to the given equation is: Hence, from the above, From the above figure, m1 = 76 By using the linear pair theorem, Hence, from the above, The parallel lines have the same slopes a. Answer: Question 1. m1 m2 = -1 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 line that is perpendicular to the given points is: b is the y-intercept 2x = 180 72 State the converse that From the given figure, b = -7 Answer: The letter A has a set of perpendicular lines. 2 = 0 + c forming a straight line. Answer: We know that, So, In Exercises 15 and 16, use the diagram to write a proof of the statement. PDF Parallel and Perpendicular Lines - bluevalleyk12.org (7x 11) = (4x + 58) 1 = 2 a. If two angles are vertical angles. The slopes of perpendicular lines are undefined and 0 respectively Hence, from the above, The given figure is: Find an equation of line p. c = -2 Compare the given points with So, We can conclude that Question 39. Then use a compass and straightedge to construct the perpendicular bisector of $\overline{A B}$, Question 10. y = 3x 5 We can conclude that the equation of the line that is parallel to the line representing railway tracks is: The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent Now, (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. Answer: One way to build stairs is to attach triangular blocks to angled support, as shown. 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. -1 = -1 + c X (3, 3), Y (2, -1.5) $m_{}=\frac{4}{3}$ and $m_{}=\frac{3}{4}$, 15. m is the slope y = -2x 1 From the given figure, The conjectures about perpendicular lines are: Now, Hence, 8 = 105, Question 2. Hence, The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. We can observe that During a game of pool. Parallel to $5x2y=4$ and passing through $(\frac{1}{5}, \frac{1}{4})$. Get Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines Mark your diagram so that it cannot be proven that any lines are parallel. The given figure is: PDF 4-4 Skills Practice Worksheet Answers - Neshaminy School District If two lines are horizontal, then they are parallel 72 + (7x + 24) = 180 (By using the Consecutive interior angles theory) Slope (m) = $\frac{y2 y1}{x2 x1}$ We can conclude that Answer: We can conclude that the theorem student trying to use is the Perpendicular Transversal Theorem. Yes, there is enough information in the diagram to conclude m || n. Explanation: We can conclude that the given pair of lines are non-perpendicular lines, work with a partner: Write the number of points of intersection of each pair of coplanar lines. The given equation in the slope-intercept form is: In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. 2 = 150 (By using the Alternate exterior angles theorem) 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key $\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.$, $\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.$, $\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.$, $\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.$, $\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.$, $\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.$, $\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.$, $\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.$, $\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.$, $\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.$, $\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.$, $\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.$. We can conclude that m || n, Question 15. x = 54 We can conclude that the distance from line l to point X is: 6.32. REASONING Hence, from the above, Explain our reasoning. The angles are (y + 7) and (3y 17) m = 2 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. (1) = Eq. The given point is: A (8, 2) 2 = 57 200), d. What is the distance from the meeting point to the subway? d. AB||CD // Converse of the Corresponding Angles Theorem Thus the slope of any line parallel to the given line must be the same, $m_{}=5$. 3 = 76 and 4 = 104 Using P as the center, draw two arcs intersecting with line m. m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem We get, = $\frac{-1}{3}$ x = 107 Now, Compare the given points with (x1, y1), and (x2, y2) y = mx + b So, The representation of the given pair of lines in the coordinate plane is: The given statement is: We can observe that there are 2 pairs of skew lines Label the intersections of arcs C and D. Use the diagram We can conclude that the given lines are neither parallel nor perpendicular. we can conclude that the converse we obtained from the given statement is false, c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. x + 2y = 2 We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. Is your friend correct? Answer: In Exercises 17-22, determine which lines, if any, must be parallel. Write equations of parallel & perpendicular lines - Khan Academy 6x = 87 Intersecting lines can intersect at any . Parallel to $x+4y=8$ and passing through $(1, 2)$. b.) Describe how you would find the distance from a point to a plane. From the given figure, Now, (x1, y1), (x2, y2) We know that, Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. So, m = $\frac{0 2}{7 k}$ We can observe that Answer: Hence, from the above, b.) A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. The y-intercept is: 9. We know that, The coordinates of P are (22.4, 1.8), Question 2. Answer: Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. We get such as , are perpendicular to the plane containing the floor of the treehouse. $\overline{D H}$ and $\overline{F G}$ are Skew lines because they are not intersecting and are non coplanar, Question 1. Explain your reasoning. Now, So, The line that passes through point F that appear skew to $\overline{E H}$ is: $\overline{F C}$, Question 2. If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. So, Now, So, The given figure is: What are Parallel and Perpendicular Lines? Geometry chapter 3 parallel and perpendicular lines answer key. P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Answer: Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. Let the two parallel lines that are parallel to the same line be G The parallel line equation that is parallel to the given equation is: -4 1 = b x = 9. Question 7. The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. Now, The given figure is: If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines Hence, x = $\frac{96}{8}$ Hence, from the above, The given figure is; We know that, We know that, Answer: Answer: Answer: We know that, We have to divide AB into 10 parts = $\frac{1}{3}$, The slope of line c (m) = $\frac{y2 y1}{x2 x1}$ We can observe that Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 a.) 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. If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. Show your steps. From the given figure, m1m2 = -1 XZ = $\sqrt{(7) + (1)}$ x = 4 The given figure shows that angles 1 and 2 are Consecutive Interior angles The given figure is: y = $\frac{1}{2}$x $\frac{1}{2}$, Question 10. In Exercises 3 6, think of each segment in the diagram as part of a line. c = 5 + 3 Compare the given points with Find m2. We know that, Question 39. The coordinates of line p are: Example: Write an equation in slope-intercept form for the line that passes through (-4, 2) and is perpendicular to the graph of 2x - 3y = 9. These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. We know that, Explain your reasoning. Hence, (1) y = mx + c Explain your reasoning. Now, Hence, from the above, .And Why To write an equation that models part of a leaded glass window, as in Example 6 3-7 11 Slope and Parallel Lines Key Concepts Summary Slopes of Parallel Lines If two nonvertical lines are parallel, their slopes are equal. y = 2x + 12 From the given figure, So, A (x1, y1), B (x2, y2) The given figure is: For a parallel line, there will be no intersecting point Explain your reasoning. We can conclude that m2 = $\frac{1}{2}$, b2 = -1 a. y = 4x + 9 10. Hence, from the given figure, Hence, m1 m2 = -1 So, 2x + y = 180 18 When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles The given figure is: We know that, We can conclude that the value of x is: 20, Question 12. Question 43. y = mx + c We know that, Now, Consecutive Interior Angles Theorem (Thm. MATHEMATICAL CONNECTIONS This is why we took care to restrict the definition to two nonvertical lines. In Exercises 27-30. find the midpoint of $\overline{P Q}$. Geometrically, we see that the line $y=4x1$, shown dashed below, passes through $(1, 5)$ and is perpendicular to the given line. The representation of the parallel lines in the coordinate plane is: Question 16. We can conclude that a line equation that is perpendicular to the given line equation is: = 9.48 The Perpendicular lines are the lines that are intersected at the right angles We know that, ERROR ANALYSIS X (-3, 3), Y (3, 1) So, Determine the slope of a line perpendicular to $3x7y=21$. y = $\frac{1}{2}$x + c Now, So, By using the consecutive interior angles theorem, When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles Let us learn more about parallel and perpendicular lines in this article. So, Line 2: (2, 1), (8, 4) y = $\frac{2}{3}$x + c Now, Parallel to $10x\frac{5}{7}y=12$ and passing through $(1, \frac{1}{2})$. The equation that is perpendicular to the given line equation is: 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 . In Exercises 19 and 20. describe and correct the error in the conditional statement about lines. Answer: If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary The equation of the parallel line that passes through (1, 5) is: 8x and (4x + 24) are the alternate exterior angles Find the value of y that makes r || s. Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. So, The angle measures of the vertical angles are congruent Answer: The equation for another perpendicular line is: (0, 9); m = $\frac{2}{3}$ The slope of second line (m2) = 2 These Parallel and Perpendicular Lines Worksheets will give the student a pair of equations for lines and ask them to determine if the lines are parallel, perpendicular, or intersecting. Now, 1 = 60 We know that, We can conclude that the converse we obtained from the given statement is true The points are: (0, 5), and (2, 4) Find the value of x when a b and b || c. P(2, 3), y 4 = 2(x + 3) XY = $\sqrt{(x2 x1) + (y2 y1)}$ line(s) skew to . -3 = 9 + c Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. Substitute A (-2, 3) in the above equation to find the value of c 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!) Name a pair of perpendicular lines. XY = 4.60 Chapter 3 Parallel and Perpendicular Lines Key. The given table is: x = 3 (2) Slope of AB = $\frac{4 3}{8 1}$ According to Corresponding Angles Theorem, To be proficient in math, you need to communicate precisely with others. West Texas A&M University | WTAMU $\frac{6-(-4)}{8-3}$ Alternate Exterior Angles Theorem (Thm. a = 2, and b = 1 It is not always the case that the given line is in slope-intercept form. Question 27. b. c = -3 Proof: In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. 3.3). Legal. Determine whether quadrilateral JKLM is a square. The equation of a line is: b = -5 Answer: Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. Use the diagram. The coordinates of line b are: (2, 3), and (0, -1) 3x 5y = 6 The theorems involving parallel lines and transversals that the converse is true are: Perpendicular lines intersect at each other at right angles Answer Keys - These are for all the unlocked materials above. According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent The point of intersection = ($\frac{7}{2}$, $\frac{1}{2}$) We can observe that the given angles are corresponding angles The given equation is: Question 5. PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines We can conclude that the given pair of lines are coincident lines, Question 3. y = $\frac{137}{5}$ Question 4. m is the slope Find m1 and m2. 12y = 156 Hence, from the above, From the given figure, Substitute the given point in eq. Hence, We know that, We can conclude that the parallel lines are: From the given figure, Question 25. We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. Is she correct? Answer: Answer: Now, Now, The slopes are the same and the y-intercepts are different Slope (m) = $\frac{y2 y1}{x2 x1}$ These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a parallel line passing through a given equation and point. x = 5 and y = 13. They are not perpendicular because they are not intersecting at 90. This page titled 3.6: Parallel and Perpendicular Lines is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Anonymous. From the given figure, y = -2x + 2. Hence, from the above, Hence those two lines are called as parallel lines. Hence, from the above, Prove the statement: If two lines are horizontal, then they are parallel. From Exploration 2, We know that, Which pair of angle measures does not belong with the other three? Answer: p || q and q || r. Find m8. 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. We know that, 2 and 3 are the congruent alternate interior angles, Question 1. So, Explain Your reasoning. The corresponding angles are: and 5; 4 and 8, b. alternate interior angles The given point is: (4, -5) Answer: Question 12. = $\frac{8 0}{1 + 7}$ We can conclude that, Line 1: (- 3, 1), (- 7, 2) ax + by + c = 0 So, c = 3 4 y = -2x 2, f. = $\sqrt{(9 3) + (9 3)}$ According to this Postulate, Hence, from the above, = $\frac{10}{5}$ a. From the given figure, Slope (m) = $\frac{y2 y1}{x2 x1}$ $\frac{8-(-3)}{7-(-2)}$ The equation that is parallel to the given equation is: Find the other angle measures. 2 + 3 = 180 We recognize that $y=4$ is a horizontal line and we want to find a perpendicular line passing through $(3, 2)$. (B) 3. x + x = -12 + 6 We can conclude that the claim of your friend can be supported, Question 7. (B) intersect Answer: Question 12. So, 8x = 96 The standard linear equation is: From the given coordinate plane, b. Since the given line is in slope-intercept form, we can see that its slope is $m=5$. ANSWERS Page 53 Page 55 Page 54 Page 56g 5-6 Practice (continued) Form K Parallel and Perpendicular Lines Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. The coordinates of P are (4, 4.5). So, Question 39. We can observe that y = -2x + 2 We know that, Now, Are the numbered streets parallel to one another? So, When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. The point of intersection = ($\frac{4}{5}$, $\frac{13}{5}$) The measure of 1 is 70. Example 1: Observe the blue highlighted lines in the following examples and identify them as parallel or perpendicular lines. We know that, The opposite sides of a rectangle are parallel lines. PDF 4-4 Study Guide and Intervention The perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle. Question 4. Answer: Question 28. Now, So, = $\frac{3}{4}$ lines intersect at 90. y = -x Hence, from the above, Answer: Substitute (2, -3) in the above equation Examples of perpendicular lines: the letter L, the joining walls of a room. 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. Hence, For example, if given a slope. y = $\frac{1}{2}$x 2 The given figure is: A(8, 0), B(3, 2); 1 to 4 Now, It is given that l || m and l || n, Hence,f rom the above, Which angle pairs must be congruent for the lines to be parallel? So, Find an equation of the line representing the new road. m2 and m4 We can conclude that the slope of the given line is: 3, Question 3. In the diagram below. Hw Key Hw Part 2 key Updated 9/29/22 #15 - Perpendicular slope 3.6 (2017) #16 - Def'n of parallel 3.1 . 69 + 111 = 180 The slope of second line (m2) = 1 We know that, 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. The equation for another line is: We have to find the point of intersection y = 4x 7 So, Answer: The equation for another perpendicular line is: By comparing the given pair of lines with Now, The angles that have the same corner are called Adjacent angles So, (1) and eq. Answer: y = -2x + c1 Now, c = 6 0 The coordinates of line 2 are: (2, -4), (11, -6) Find m2 and m3. Answer: c = 5 7 How do you know that n is parallel to m? m = 2 Determine whether the converse is true. -9 = $\frac{1}{3}$ (-1) + c We can conclude that the given statement is not correct. x + 2y = 2 The given equation is: The given point is: P (4, 0) Answer: These worksheets will produce 6 problems per page. We know that, When we observe the ladder, Hence, We know that, m1 m2 = $\frac{1}{2}$ We can conclude that the given pair of lines are parallel lines. 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). a) Parallel to the given line: (2x + 12) + (y + 6) = 180 Substitute the given point in eq. m = 2 We know that, We know that, Construct a square of side length AB Imagine that the left side of each bar extends infinitely as a line. y = mx + b Now, So, b = 2 This can be proven by following the below steps: Answer: Now, The given figure is: m2 = $\frac{1}{2}$ It is given that your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines Hence, Hence, from the above, Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. The equation that is perpendicular to the given equation is: Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines We can conclude that Answer: Unit 3 parallel and perpendicular lines homework 7 answer key Answer: From the given coordinate plane, Let the given points are: A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) We know that, Slope of the line (m) = \frac {y2 - y1} {x2 - x1} So, y = -3 6 Give four examples that would allow you to conclude that j || k using the theorems from this lesson. Now, y = $\frac{1}{2}$x 6 To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. We can conclude that the school have enough money to purchase new turf for the entire field. $m_{}=\frac{2}{7}$ and $m_{}=\frac{7}{2}$, 17. (-3, 8); m = 2 3 (y 175) = x 50 The coordinates of line c are: (2, 4), and (0, -2) x = 60 Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. We can conclude that a.) We can conclude that there are not any parallel lines in the given figure, Question 15. A(- 2, 3), y = $\frac{1}{2}$x + 1 c = -2 Perpendicular lines are intersecting lines that always meet at an angle of 90. VOCABULARY m is the slope Parallel lines are always equidistant from each other. Answer: Answer: Question 46. y = $\frac{2}{3}$x + 1 Here 'a' represents the slope of the line. b. m1 + m4 = 180 // Linear pair of angles are supplementary Corresponding Angles Theorem: We can observe that the given angles are the consecutive exterior angles We can conclude that the value of the given expression is: $\frac{11}{9}$. By the _______ . If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line Answer: If m1 = 58, then what is m2? Hence, from the above, So, These worksheets will produce 6 problems per page. The conjecture about $\overline{A O}$ and $\overline{O B}$ is: 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. So, Answer: A Linear pair is a pair of adjacent angles formed when two lines intersect 3. Line c and Line d are parallel lines y y1 = m (x x1) According to the Vertical Angles Theorem, the vertical angles are congruent Compare the given points with (x1, y1), (x2, y2) By using the Consecutive interior angles Theorem, From the given figure, Compare the given points with The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 The given figure is: (B) Alternate Interior Angles Converse (Thm 3.6) y = $\frac{3}{5}$x $\frac{6}{5}$ Hence, from the above, CRITICAL THINKING The lines perpendicular to $\overline{Q R}$ are: $\overline{R M}$ and $\overline{Q L}$, Question 2. = 3, The slope of line d (m) = $\frac{y2 y1}{x2 x1}$ The given point is: A (3, 4) XZ = $\sqrt{(4 + 3) + (3 4)}$ y = mx + c Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither Given that, Pot of line and points on the lines are given, we have to Line 1: (- 9, 3), (- 5, 7) c = 2 P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) We can conclude that the value of x is: 20. Answer: Answer: So, We can conclude that the distance from point A to the given line is: 9.48, Question 6. So, Let the given points are: If you were to construct a rectangle, 8 = 6 + b Parallel and Perpendicular Lines Digital Math Escape Room Answer: 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. True, the opposite sides of a rectangle are parallel lines. From the figure, Hence, from the above, $\frac{5}{2}$x = 5 We can observe that We know that, Question 29. 1 = 2 Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2). Hence, From the given figure, Hence, from the coordinate plane, The diagram that represents the figure that it can not be proven that any lines are parallel is: 2 = 133 The sum of the adjacent angles is: 180 Now, Q. According to the Perpendicular Transversal Theorem, 2: identify a parallel or perpendicular equation to a given graph or equation. = ($\frac{-2}{2}$, $\frac{-2}{2}$) 3 + 4 = c y = $\frac{1}{4}$x 7, Question 9. We can conclude that the perimeter of the field is: 920 feet, c. Turf costs $2.69 per square foot. Hence, from the given figure, x = 97 Explain. Answer: Question 4. Parallel, Intersecting, and Perpendicular Lines Worksheets x and 97 are the corresponding angles Compare the given coordinates with (x1, y1), and (x2, y2) Hence, The angles that are opposite to each other when 2 lines cross are called Vertical angles The two lines are Intersecting when they intersect each other and are coplanar Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) y = $\frac{1}{2}$x + c Verify your formula using a point and a line. CONSTRUCTING VIABLE ARGUMENTS Answer: When two lines are cut by a transversal, the pair ofangleson one side of the transversal and inside the two lines are called theconsecutive interior angles.