parallel and perpendicular lines answer key

The equation for another perpendicular line is: In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m. Question 10. Slope of ST = $\frac{2}{-4}$ y = $\frac{3}{2}$ = $\frac{0}{4}$ M = (150, 250), b. Hence, from the above, Answer: Substitute (-2, 3) in the above equation y = -2x + 8 The letter A has a set of perpendicular lines. c = $\frac{16}{3}$ 2 = 150 (By using the Alternate exterior angles theorem) We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. Explain your reasoning? d = $\sqrt{(x2 x1) + (y2 y1)}$ What are the coordinates of the midpoint of the line segment joining the two houses? The given line that is perpendicular to the given points is: Slope of QR = $\frac{1}{2}$, Slope of RS = $\frac{1 4}{5 6}$ Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. We know that, Since, Slope of LM = $\frac{0 n}{n n}$ We can say that all the angle measures are equal in Exploration 1 We have to find 4, 5, and 8 then they intersect to form four right angles. y = mx + c Question 22. Label the intersections of arcs C and D. d. AB||CD // Converse of the Corresponding Angles Theorem 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 We can conclude that the value of x is: 133, Question 11. This contradicts what was given,that angles 1 and 2 are congruent. The lines that are at 90 are Perpendicular lines Explain your reasoning. Slope of the line (m) = $\frac{y2 y1}{x2 x1}$ Hence, from the above, d. AB||CD // Converse of the Corresponding Angles Theorem m2 = $\frac{2}{3}$ Explain your reasoning. It is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet. b = 9 ABSTRACT REASONING Answer: The given equation is: Answer: 3 = 47 Bertha Dr. is parallel to Charles St. The product of the slopes of the perpendicular lines is equal to -1 To find the value of c in the above equation, substitue (0, 5) in the above equation Answer: c. m5=m1 // (1), (2), transitive property of equality We know that, Negative reciprocal means, if m1 and m2 are negative reciprocals of each other, their product will be -1. By comparing the slopes, The postulates and theorems in this book represent Euclidean geometry. Answer: Question 31. The slopes of perpendicular lines are undefined and 0 respectively BCG and __________ are consecutive interior angles. Part 1: Determine the parallel line using the slope m = {2 \over 5} m = 52 and the point \left ( { - 1, - \,2} \right) (1,2). y = 2x 2. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. We know that, Hence, from the above, y = $\frac{1}{2}$x 2 y = $\frac{1}{2}$x 3 2 and7 The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, Answer: Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? From the given figure, Compare the given points with (x1, y1), and (x2, y2) So, From the above definition, x = 54 The product of the slopes of the perpendicular lines is equal to -1 So, So, Answer: We can observe that Is your classmate correct? b) Perpendicular to the given line: MODELING WITH MATHEMATICS Compare the given coordinates with We know that, Question 13. -2 = 3 (1) + c We can observe that $\overline{A C}$ is not perpendicular to $\overline{B F}$ because according to the perpendicular Postulate, $\overline{A C}$ will be a straight line but it is not a straight line when we observe Example 2 The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent MODELING WITH MATHEMATICS Solution: We need to know the properties of parallel and perpendicular lines to identify them. We can conclude that the length of the field is: 320 feet, b. Now, y = $\frac{1}{2}$x 2 We know that, as shown. Now, Hence, from the above, (50, 175), (500, 325) y = x 6 Hence, from the above, d = | 6 4 + 4 |/ $\sqrt{2}$} So, We know that, y = 2x + c Hence, from the above, d = $\sqrt{(x2 x1) + (y2 y1)}$ So, The given equation is: Proof: We know that, y = $\frac{1}{2}$x + 2 We know that, 2 and 4 are the alternate interior angles Answer: The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. Answer: Parallel to $10x\frac{5}{7}y=12$ and passing through $(1, \frac{1}{2})$. 1 + 2 = 180 Hence, PROBLEM-SOLVING m1m2 = -1 Now, What is the distance between the lines y = 2x and y = 2x + 5? 3.12) Hence, from the above, (1) = Eq. From the given coordinate plane, Find the slope $m$ by solving for $y$. 12. If we draw the line perpendicular to the given horizontal line, the result is a vertical line. The equation of a line is: If you were to construct a rectangle, Hence. REASONING y = $\frac{1}{2}$x + c 6x = 87 Hence, from the given figure, such as , are perpendicular to the plane containing the floor of the treehouse. Justify your answer. So, Use a graphing calculator to graph the pair of lines. These worksheets will produce 10 problems per page. -1 = $\frac{-2}{7 k}$ y = 12 If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel (A) are parallel. We were asked to find the equation of a line parallel to another line passing through a certain point. We can conclude that the slope of the given line is: $\frac{-3}{4}$, Question 2. We know that, We know that, So, We know that, So, Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. Here is a quick review of the point/slope form of a line. Determine the slope of parallel lines and perpendicular lines. From the given figure, Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. y = $\frac{1}{2}$x + c Line 1: (1, 0), (7, 4) Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines Compare the given points with (x1, y1), and (x2, y2) The slope of line a (m) = $\frac{y2 y1}{x2 x1}$ 2 = 180 123 2 ________ by the Corresponding Angles Theorem (Thm. Alternate Exterior angle Theorem: These worksheets will produce 6 problems per page. Question 27. 5 = 3 (1) + c In Exercises 7-10. find the value of x. (5y 21) = 116 Through the point $(6, 1)$ we found a parallel line, $y=\frac{1}{2}x4$, shown dashed. The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. The given statement is: So, 48 + y = 180 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. So, COMPLETE THE SENTENCE From the given figure, (180 x) = x = 2.23 y = $\frac{1}{7}$x + 4 We recognize that $y=4$ is a horizontal line and we want to find a perpendicular line passing through $(3, 2)$. Use a graphing calculator to verify your answers. Answer: The given figure is: y = 2x + c Hence, from the above, x = 29.8 Answer: For example, if given a slope. Ruler: The highlighted lines in the scale (ruler) do not intersect or meet each other directly, and are the same distance apart, therefore, they are parallel lines. 4 6 = c To find the value of c, Prove the statement: If two lines are vertical. AP : PB = 3 : 2 Classify each pair of angles whose measurements are given. x = n A (x1, y1), and B (x2, y2) We know that, We can observe that We know that, So, Hence, from the above, The given figure is: (D) Consecutive Interior Angles Converse (Thm 3.8) Often you have to perform additional steps to determine the slope. y = $\frac{1}{2}$x 4, Question 22. transv. 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 Solve eq. Answer: The given point is: (1, 5) line(s) skew to Answer: ax + by + c = 0 (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. Answer: Apply slope formula, find whether the lines are parallel or perpendicular. AP : PB = 4 : 1 X (-3, 3), Y (3, 1) Name two pairs of congruent angles when $\overline{A D}$ and $\overline{B C}$ are parallel? Answer: Question 18. So, Using the same compass selling, draw an arc with center B on each side $\overline{A B}$. The painted line segments that brain the path of a crosswalk are usually perpendicular to the crosswalk. Hence, from the above, To find the coordinates of P, add slope to AP and PB (- 3, 7) and (8, 6) So, b) Perpendicular line equation: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Yes, your classmate is correct, Explanation: Hence,f rom the above, Let the given points are: Question 21. The diagram can be changed by the transformation of transversals into parallel lines and a parallel line into transversal Hence, Mark your diagram so that it cannot be proven that any lines are parallel. 1 + 18 = b (x1, y1), (x2, y2) y = mx + c In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use. Given that, Pot of line and points on the lines are given, we have to = $\sqrt{31.36 + 7.84}$ Answer: y = -7x + c a. To find the value of c, Answer: Question 24. The given figure is: y = $\frac{1}{2}$x + b (1) So, The general steps for finding the equation of a line are outlined in the following example. Question 25. so they cannot be on the same plane. So, c.) Parallel lines intersect each other at 90. c. If m1 is 60, will ABC still he a straight angle? We can say that Hence, Examples of perpendicular lines: the letter L, the joining walls of a room. Label its intersection with $\overline{A B}$ as O. Answer: Using the properties of parallel and perpendicular lines, we can answer the given questions. Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. Answer: The equation that is perpendicular to the given equation is: x = y = 61, Question 2. Which values of a and b will ensure that the sides of the finished frame are parallel.? So, c is the y-intercept 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. Hence, from the above, So, Write an equation of the line that passes through the point (1, 5) and is So, Example 5: Tell whether the line y = {4 \over 3}x + 2 y = 34x + 2 is parallel, perpendicular or neither to the line passing through \left ( {1,1} \right) (1,1) and \left ( {10,13} \right) (10,13). Prove 1, 2, 3, and 4 are right angles. We know that, So, We can conclude that the slope of the given line is: 3, Question 3. Now, Draw a diagram of at least two lines cut by at least one transversal. The distance between the perpendicular points is the shortest y = -2x 1 Now, If two lines are parallel to the same line, then they are parallel to each other What can you conclude about the four angles? then they are parallel. We know that, To find the coordinates of P, add slope to AP and PB m1m2 = -1 Hence, from the given figure, First, find the slope of the given line. So, We can conclude that the distance from point A to the given line is: 5.70, Question 5. Hence, from the above, From the given figure, Legal. 132 = (5x 17) y = 3x + 2, (b) perpendicular to the line y = 3x 5. The given figure is: $m_{}=4$ and $m_{}=\frac{1}{4}$, 5. Find an equation of the line representing the new road. (1) = Eq. So, The equation for another parallel line is: The given parallel line equations are: a. Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). x y = 4 3.3). Answer: Hence, from the above, Answer: We can conclude that 1 and 5 are the adjacent angles, Question 4. PROBLEM-SOLVING Now, We can conclude that The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line Hence, from the above, The slope of the given line is: m = $\frac{2}{3}$ 2x = 180 72 c = 0 2. The given figure is: For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts XY = $\sqrt{(x2 x1) + (y2 y1)}$ The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles Slope of line 2 = $\frac{4 6}{11 2}$ y = 2x + c1 x = 147 14 Now, Two lines that do not intersect and are also not parallel are ________ lines. The Converse of the Alternate Exterior Angles Theorem: So, y = mx + b From the given figure, The given equation is: In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? 8 = 105, Question 2. To find the value of c, 2: identify a parallel or perpendicular equation to a given graph or equation. In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. MAKING AN ARGUMENT In Exercise 31 on page 161, from the coordinate plane, Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. Answer: If you go to the zoo, then you will see a tiger y = -3 The converse of the given statement is: Hence, from the above, Hence, from the above figure, $\frac{5}{2}$x = 5 Hence, from the above, So, Each step is parallel to the step immediately above it. If it is warm outside, then we will go to the park answer choices y = -x + 4 y = x + 6 y = 3x - 5 y = 2x Question 6 300 seconds Q. We know that, Given: k || l By using the Corresponding angles Theorem, We can conclude that the pair of perpendicular lines are: Hence, from the above, d = $\sqrt{290}$ y = mx + b We know that, Now, 7 = -3 (-3) + c 2x y = 4 We know that, PROOF y = 0.66 feet 1 = 0 + c So, Label the intersection as Z. Explain why the top rung is parallel to the bottom rung. Hence, The given equations are: Is she correct? The given table is: Answer: Substitute A (6, -1) in the above equation d = | 2x + y | / $\sqrt{5}$} We can observe that 0 = $\frac{1}{2}$ (4) + c Answer: We know that, In Exploration 2. m1 = 80. The following table shows the difference between parallel and perpendicular lines. Substitute P (4, 0) in the above equation to find the value of c Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive y1 = y2 = y3 Slope of QR = $\frac{-2}{4}$ When you look at perpendicular lines they have a slope that are negative reciprocals of each other. In other words, if $m=\frac{a}{b}$, then $m_{}=\frac{b}{a}$. We can observe that when r || s, it is given that the turf costs $2.69 per square foot Where, Answer: Substitute A (3, 4) in the above equation to find the value of c The bottom step is parallel to the ground. The given figure is: Justify your answers. From the given figure, We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. The given figure is: If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. Geometry chapter 3 parallel and perpendicular lines answer key. We can observe that the length of all the line segments are equal MATHEMATICAL CONNECTIONS Hence, from the above, Now, Substitute (1, -2) in the above equation 3 + 4 = c To find the value of c, Perpendicular to $5x+y=1$ and passing through $(4, 0)$. Hence, from the above, We can observe that there are 2 perpendicular lines Compare the given points with Each rung of the ladder is parallel to the rung directly above it. i.e., Hence,f rom the above, In this form, you can see that the slope is $m=2=\frac{2}{1}$, and thus $m_{}=\frac{1}{2}=+\frac{1}{2}$. The coordinates of the meeting point are: (150. Converse: The given figure is: We can conclude that 44 and 136 are the adjacent angles, b. MATHEMATICAL CONNECTIONS a) Parallel line equation: 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation $m_{}$ reads $m$ perpendicular. We can verify that two slopes produce perpendicular lines if their product is $1$. Compare the given equation with 68 + (2x + 4) = 180 The representation of the given point in the coordinate plane is: Question 56. Answer: Question 4. We can conclude that 1 2. m2 = -1 Answer: y = -3x + c So, y = $\frac{1}{3}$x 2. Compare the given points with c = 7 If you go to the zoo, then you will see a tiger. (x1, y1), (x2, y2) Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. So, So, 17x + 27 = 180 2x + y + 18 = 180 Question 5. Answer: Yes, there is enough information in the diagram to conclude m || n. Explanation: From the given figure, Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. Compare the given points with By using the linear pair theorem, Now, m = $\frac{3 0}{0 + 1.5}$ i.e., A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. x = 9 m2 = -3 P(4, 0), x + 2y = 12 $\frac{8-(-3)}{7-(-2)}$ Answer: Question 16. If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. We can conclude that the value of x is: 23. We can observe that, 4 and 5 y = $\frac{7}{2}$ 3 Justify your conjecture. We have to find the point of intersection Construct a square of side length AB Hence, from the above, Q. We can observe that the product of the slopes are -1 and the y-intercepts are different We can observe that there are a total of 5 lines. 2 = 133 $\overline{C D}$ and $\overline{A E}$ (2) We can conclude that the distance from point A to the given line is: 9.48, Question 6. By using the linear pair theorem, To find 4: 20 = 3x 2x Do you support your friends claim? = 2 (2) Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Perpendicular to $y=2x+9$ and passing through $(3, 1)$. 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XY = $\sqrt{(6) + (2)}$ The given point is: A (3, -4) We know that, y = -x + c Hence, The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. Slope of AB = $\frac{1 + 4}{6 + 2}$ The given figure is: Now, In the diagram below. c = $\frac{8}{3}$ Answer: Perpendicular Transversal Theorem A carpenter is building a frame. Answer: So, PROVING A THEOREM We know that, So, = 104 Describe how you would find the distance from a point to a plane. y = $\frac{1}{2}$x + 7 Hence, from the above, = $\sqrt{(9 3) + (9 3)}$ x = $\frac{120}{2}$ We can conclude that if you use the third statement before the second statement, you could still prove the theorem, Question 4. The plane parallel to plane ADE is: Plane GCB. For parallel lines, By using the Corresponding Angles Theorem, The midpoint of PQ = ($\frac{x1 + x2}{2}$, $\frac{y1 + y2}{2}$) The equation that is parallel to the given equation is: Fro the given figure, c. m5=m1 // (1), (2), transitive property of equality 2x = -6 We can conclude that Two lines are cut by a transversal. So, d = $\sqrt{(x2 x1) + (y2 y1)}$ The given figure is: If the pairs of corresponding angles are, congruent, then the two parallel lines are. So, So, Answer: Question 32. Hence, from the above, It is not always the case that the given line is in slope-intercept form. We know that, ($\frac{1}{2}$) (m2) = -1 If the slopes of the opposite sides of the quadrilateral are equal, then it is called as Parallelogram If two intersecting lines are perpendicular. When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. COMPLETE THE SENTENCE We know that, According to the Perpendicular Transversal Theorem, Now, So, So, y = 3x 6, Question 20. We know that, The given equation of the line is: Answer: (2, 7); 5 1 2 11 CONSTRUCTING VIABLE ARGUMENTS It is given that a student claimed that j K, j l WRITING We can conclude that the number of points of intersection of coincident lines is: 0 or 1.