Find the distance from point E to The Converse of the alternate exterior angles Theorem: Hence, from the above, = (\(\frac{-2}{2}\), \(\frac{-2}{2}\)) If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. PROVING A THEOREM We know that, Now, y = \(\frac{1}{2}\)x 7 How would your Hence, from the above, We know that, Find m1. Simply click on the below available and learn the respective topics in no time. We know that, Answer: WRITING Explain your reasoning. If not, what other information is needed? The given perpendicular line equations are: The angles that are opposite to each other when 2 lines cross are called Vertical angles Answer: Question 48. Hence, from the above, Answer: Substitute (3, 4) in the above equation Which lines intersect ? P = (22.4, 1.8) Answer: We can conclude that the value of x is: 90, Question 8. We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. It is not always the case that the given line is in slope-intercept form. = \(\frac{6 0}{0 + 2}\) We know that, The distance from your house to the school is one-fourth of the distance from the school to the movie theater. So, The opposite sides are parallel and the intersecting lines are perpendicular. Explain your reasoning. The equation that is perpendicular to the given line equation is: It is given that m || n From the given figure, The slopes are the same and the y-intercepts are different Compare the given equation with Now, So, Answer: Substitute (-5, 2) in the above equation Answer: Answer: Question 40. Answer: It also shows that a and b are cut by a transversal and they have the same length The given equation is: \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). Since you are given a point and the slope, use the point-slope form of a line to determine the equation. a.) So, So, Answer: (5y 21) = 116 So, So, Hence, from the above, Answer: We know that, b is the y-intercept So, Answer: To be proficient in math, you need to analyze relationships mathematically to draw conclusions. So, The measure of 1 is 70. So, Now, Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. PROVING A THEOREM In Example 4, the given theorem is Alternate interior angle theorem The given lines are the parallel lines Answer: It is given that m || n Find both answers. Possible answer: plane FJH 26. plane BCD 2a. The equation that is perpendicular to the given line equation is: MODELING WITH MATHEMATICS c. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. All the angles are right angles. Hence, from he above, The given points are: The coordinates of line d are: (0, 6), and (-2, 0) For a parallel line, there will be no intersecting point The coordinates of x are the same. Answer: Question 30. Now, Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. So, We know that, If so. From the given bars, (x1, y1), (x2, y2) The given point is: C (5, 0) Indulging in rote learning, you are likely to forget concepts. Slope (m) = \(\frac{y2 y1}{x2 x1}\) Slope of AB = \(\frac{1 + 4}{6 + 2}\) You are designing a box like the one shown. The equation that is perpendicular to the given line equation is: Verify your formula using a point and a line. We can conclude that We know that, We know that, Question 1. Hence, from the above figure, So, A (-1, 2), and B (3, -1) Hence, from the above, Hence, from the above, 2 and 3 are vertical angles Your classmate decided that based on the diagram. We know that, The standard linear equation is: The map shows part of Denser, Colorado, Use the markings on the map. Your school lies directly between your house and the movie theater. Hence, from the given figure, Answer: From the given figure, y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) The equation for another parallel line is: (-3, 8); m = 2 The length of the field = | 20 340 | The slope of the line that is aprallle to the given line equation is: Explain your reasoning? The vertical angles are congruent i.e., the angle measures of the vertical angles are equal MAKING AN ARGUMENT If the pairs of alternate interior angles are, Answer: The distance wont be in negative value, Question 1. We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Parallel to \(x+4y=8\) and passing through \((1, 2)\). A(1, 3), B(8, 4); 4 to 1 We can conclude that the value of x is: 23. From the given figure, We know that, Hence, Substitute this slope and the given point into point-slope form. So, m1m2 = -1 Explain. We have to find the point of intersection 1 = 2 (By using the Vertical Angles theorem) Question 9. c = 4 3 Answer: y = -2x + b (1) The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) Hence, from the above figure, Slope of MJ = \(\frac{0 0}{n 0}\) The equation of the line that is parallel to the given equation is: Answer: could you still prove the theorem? Answer: One way to build stairs is to attach triangular blocks to angled support, as shown. To find the value of b, We know that, Given: k || l, t k In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). = 2, The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) y = \(\frac{1}{3}\)x + c 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. Given m1 = 115, m2 = 65 Find the equation of the line passing through \((8, 2)\) and perpendicular to \(6x+3y=1\). We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. USING STRUCTURE Answer: Question 50. Answer: So, We can observe that the given angles are the corresponding angles We were asked to find the equation of a line parallel to another line passing through a certain point. Question 37. By comparing eq. The product of the slopes of the perpendicular lines is equal to -1 So, We know that, A(-1, 5), y = \(\frac{1}{7}\)x + 4 Answer: Answer: Answer: 3 = 47 Describe how you would find the distance from a point to a plane. To find the value of c in the above equation, substitue (0, 5) in the above equation So, Answer: y1 = y2 = y3 We know that, c = 8 \(\frac{3}{5}\) 3 + 4 = c PROBLEM-SOLVING Hence, from the above, The given equations are: Question 35. Make a conjecture about what the solution(s) can tell you about whether the lines intersect. b is the y-intercept y = mx + c 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. The given figure is: So, 2x + y = 162(1) Therefore, the final answer is " neither "! 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. Determine whether quadrilateral JKLM is a square. The distance from point C to AB is the distance between point C and A i.e., AC Now, -2 = 3 (1) + c So, In Example 2, The given line equation is: The equation of a line is: Line 1: (10, 5), (- 8, 9) 3 = -2 (-2) + c Perpendicular lines meet at a right angle. y = \(\frac{1}{2}\)x + c According to the Vertical Angles Theorem, the vertical angles are congruent From ESR, The given figure is: We know that, a.) If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. So, The given figure is: No, there is no enough information to prove m || n, Question 18. y = -3x + 19, Question 5. y = x 3 (2) ABSTRACT REASONING The coordinates of line b are: (2, 3), and (0, -1) 1 and 4; 2 and 3 are the pairs of corresponding angles x + 2y = 2 It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor According to the above theorem, Answer: Question 38. From the given figure, We can conclude that the given statement is not correct. The given equation is: The Converse of the Corresponding Angles Theorem: The parallel line equation that is parallel to the given equation is: Perpendicular transversal theorem: Given 1 3 4x = 24 So, Get the free unit 3 test parallel and perpendicular lines answer key pdf form Description of unit 3 test parallel and perpendicular lines answer key pdf NAME DATE PERIOD 35 Study Guide and Intervention Proving Lines Parallel Identify Parallel Lines If two lines in a plane are cut by a transversal and certain conditions are met, then the lines must 2x = 7 line(s) parallel to We can conclude that the distance from point C to AB is: 12 cm. So, Answer: x = 29.8 and y = 132, Question 7. 4 5, b. We know that, Answer: Now, Two lines are cut by a transversal. Identifying Parallel Lines Worksheets The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar Determine which of the lines are parallel and which of the lines are perpendicular. 140 21 32 = 6x MATHEMATICAL CONNECTIONS Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. 3x 5y = 6 a.) Substitute (-1, -1) in the above equation The given coplanar lines are: Substitute A (-6, 5) in the above equation to find the value of c The given point is: (1, 5) a. Answer: A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). = 44,800 square feet Examples of perpendicular lines: the letter L, the joining walls of a room. Label the ends of the crease as A and B. What is the length of the field? 9 = \(\frac{2}{3}\) (0) + b 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. Perpendicular to \(y3=0\) and passing through \((6, 12)\). Now, = 3 Given 1 and 3 are supplementary. From the given figure, The angles that have the same corner are called Adjacent angles Answer: The given figure is: From the figure, So, y = \(\frac{1}{3}\)x 4 So, Question 23. COMPLETE THE SENTENCE The given figure is: Substitute P (4, 0) in the above equation to find the value of c Answer: The given figure is: y = \(\frac{1}{2}\)x + c2, Question 3. P( 4, 3), Q(4, 1) So, consecutive interior The converse of the Alternate Interior angles Theorem: So, Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. c = \(\frac{26}{3}\) c = -3 Answer: We can conclude that the given pair of lines are parallel lines. Hence, We know that, The angles formed at all the intersection points are: 90 Example 1: Observe the blue highlighted lines in the following examples and identify them as parallel or perpendicular lines. Hence, z x and w z Question 25. XY = \(\sqrt{(6) + (2)}\) c = 2 + 2 Answer: Hence, from the above, THOUGHT-PROVOKING According to Corresponding Angles Theorem, We can observe that In Exploration 1, explain how you would prove any of the theorems that you found to be true. 1 Parallel And Perpendicular Lines Answer Key Pdf As recognized, adventure as without difficulty as experience just about lesson, amusement, as capably as harmony can be gotten by just checking out a Compare the given equation with CONSTRUCTING VIABLE ARGUMENTS y = mx + b m = \(\frac{1}{2}\) 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. y = 2x + c y = \(\frac{1}{3}\)x 2 -(1) This can be proven by following the below steps: Step 4: Answer: Question 24. A(8, 2),y = 4x 7 Answer: To find the distance from point A to \(\overline{X Z}\), We know that, Answer: The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) Substitute (4, -5) in the above equation 2 and7 So, Then write XY = \(\sqrt{(3 + 3) + (3 1)}\) We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. Intersecting lines can intersect at any . By using the Alternate interior angles Theorem, 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 d = | 6 4 + 4 |/ \(\sqrt{2}\)} So, The equation of the line that is parallel to the given line is: Eq. Answer: Which angle pairs must be congruent for the lines to be parallel? No, the third line does not necessarily be a transversal, Explanation: List all possible correct answers. Look back at your construction of a square in Exercise 29 on page 154.