parallel and perpendicular lines answer key

We know that, Lines AB and CD are not intersecting at any point and are always the same distance apart. The total cost of the turf = 44,800 2.69 In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Hence, from the above, Answer: Question 44. Answer: Solve eq. The equation for another line is: 3 + 4 + 5 = 180 Perpendicular to $y3=0$ and passing through $(6, 12)$. We know that, -5 = $\frac{1}{4}$ (-8) + b Find the measures of the eight angles that are formed. y = mx + c Answer: We know that, k 7 = -2 We know that, Hence, So, x = y =29 The given figure is: The given pair of lines are: Find the distance from point A to the given line. The given figure is: x = 14.5 So, (2x + 20) = 3x The Converse of Corresponding Angles Theorem: = $\frac{-4}{-2}$ P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) The given point is: (-1, 6) Answer: Question 21. The slope of the given line is: m = 4 The given equation in the slope-intercept form is: y = -2x + 2 Now, Perpendicular Transversal Theorem A carpenter is building a frame. c = 8 We can conclude that the value of x is: 60, Question 6. Eq. Substitute A (-2, 3) in the above equation to find the value of c The given equation is: If r and s are the parallel lines, then p and q are the transversals. Answer: According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent Answer: Answer: So, The given points are: Write an equation of the line that passes through the given point and has the given slope. Find an equation of line q. Alternate Exterior Angles Theorem (Thm. a. The completed table of the nature of the given pair of lines is: Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal. Hence, from the above, We can conclude that These Parallel and Perpendicular Lines Worksheets will give the slope of a line and ask the student to determine the slope for any line that is parallel and the slope that is perpendicular to the given line. = $\frac{-3}{-4}$ By using the Corresponding Angles Theorem, It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor We can conclude that The lines that have an angle of 90 with each other are called Perpendicular lines Question 5. For parallel lines, we cant say anything The parallel lines have the same slope We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: To find the value of c, -x x = -3 THINK AND DISCUSS 1. = $\frac{-6}{-2}$ The given figure is: m is the slope From the given figure, We get Hence, from the above, We can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel We have to find the point of intersection In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. a. a pair of skew lines y = 3x 5 It is given that the given angles are the alternate exterior angles 1 unit either in the x-plane or y-plane = 10 feet Now, The lines perpendicular to $\overline{E F}$ are: $\overline{F B}$ and $\overline{F G}$, Question 3. Eq. From the given figure, Name two pairs of congruent angles when $\overline{A D}$ and $\overline{B C}$ are parallel? 8 + 115 = 180 Now, From the given figure, A (x1, y1), and B (x2, y2) (2, 7); 5 1 2 11 The equation that is parallel to the given equation is: $\begin{aligned} 2x+14y&=7 \\ 2x+14y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ 14y&=-2x+7 \\ \frac{14y}{\color{Cerulean}{14}}&=\frac{-2x+7}{\color{Cerulean}{14}} \\ y&=\frac{-2x}{14}+\frac{7}{14} \\ y&=-\frac{1}{7}x+\frac{1}{2} \end{aligned}$. From the given figure, 1 4. The representation of the given pair of lines in the coordinate plane is: Hence, Q. In this form, you can see that the slope is $m=2=\frac{2}{1}$, and thus $m_{}=\frac{1}{2}=+\frac{1}{2}$. Now, In Exploration 2, Mark your diagram so that it cannot be proven that any lines are parallel. if two lines are perpendicular to the same line. Furthermore, the rise and run between two perpendicular lines are interchanged. The equation that is perpendicular to the given line equation is: Answer: Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. (1) The product of the slopes of perpendicular lines is equal to -1 are parallel, or are the same line. Name them. y = -2x + c1 So, Two nonvertical lines in the same plane, with slopes $m_{1}$ and $m_{2}$, are perpendicular if the product of their slopes is $1: m1m2=1$. Answer: Hence, from the above, $\frac{1}{3}$m2 = -1 From y = 2x + 5, Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting Hence, 1 4. From the given figure, The given figure is: = $\frac{9}{2}$ XY = 6.32 We can observe that the plane parallel to plane CDH is: Plane BAE. We know that, The standard form of the equation is: We can conclude that the converse we obtained from the given statement is true The given point is: (6, 4) Draw $\overline{P Z}$, Question 8. Given m1 = 105, find m4, m5, and m8. Hence, from the above, P = (3.9, 7.6) The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. Hence, from the above, Now, y = mx + b 7x 4x = 58 + 11 It can also help you practice these theories by using them to prove if given lines are perpendicular or parallel. y = $\frac{2}{3}$x + 1 Answer: Question 12. Hence, from the above, 3x = 69 Hence, from the above, The line that is perpendicular to y=n is: The coordinates of line a are: (0, 2), and (-2, -2) x = $\frac{18}{2}$ The given figure is: The distance between lines c and d is y meters. In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. = $\sqrt{(250 300) + (150 400)}$ How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior So, Draw $\overline{A B}$, as shown. line(s) skew to So, These worksheets will produce 6 problems per page. 2 and 3 are the consecutive interior angles From the given figure, The perpendicular lines have the product of slopes equal to -1 x + x = -12 + 6 Hence, from the above, Parallel to $\frac{1}{5}x\frac{1}{3}y=2$ and passing through $(15, 6)$. Hence, Answer: Answer: Answer: The given figure shows that angles 1 and 2 are Consecutive Interior angles In Exploration 3. find AO and OB when AB = 4 units. c = 2 0 The given equation in the slope-intercept form is: The given line equation is: 3m2 = -1 Then by the Transitive Property of Congruence (Theorem 2.2), _______ . So, Answer: -2 = 0 + c We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6. If the slope of AB and CD are the same value, then they are parallel. (2x + 2) = (x + 56) -2 $\frac{2}{3}$ = c The given equation is: The Intersecting lines are the lines that intersect with each other and in the same plane Question 1. In Exercises 11-14, identify all pairs of angles of the given type. The angles formed at all the intersection points are: 90 ERROR ANALYSIS The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) which ones? $m_{}=4$ and $m_{}=\frac{1}{4}$, 5. Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. Slope of LM = $\frac{0 n}{n n}$ Answer: Question 38. From the argument in Exercise 24 on page 153, (13, 1), and (9, -4) These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel lines from pictures. b = 19 Prove: t l. PROOF So, The given statement is: The angle measures of the vertical angles are congruent So, The Perpendicular lines are the lines that are intersected at the right angles Answer: The given figure is: 3 = 68 and 8 = (2x + 4) Perpendicular lines are lines in the same plane that intersect at right angles ($90$ degrees). A(15, 21), 5x + 2y = 4 a. m5 + m4 = 180 //From the given statement c. y = 5x + 6 = $\sqrt{(9 3) + (9 3)}$ So, So, = 1.67 To find the value of c, substitute (1, 5) in the above equation Hence, from the above, as shown. 5 = -7 ( -1) + c Slope (m) = $\frac{y2 y1}{x2 x1}$ So, We know that, Question 9. 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. Hence, from the above, The given table is: Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 (b) perpendicular to the given line. The lines that are a straight angle with the given line and are coplanar is called Perpendicular lines By using the corresponding angles theorem, = $\frac{1}{3}$ Slope of the line (m) = $\frac{y2 y1}{x2 x1}$ Question 5. Question: ID Unit 3: Paraliel& Perpendicular Lines Homework 3: Proving Lines are Parolel Nome: Dnceuea pennon Per Date This is a 2-poge document Determine Im based on the intormation alven on the diogram yes, state the coverse that proves the ines are porollel 2 4. x = 90 c = -9 3 Parallel and perpendicular lines have one common characteristic between them. The two lines are vertical lines and therefore parallel. Slope (m) = $\frac{y2 y1}{x2 x1}$ We know that, Indulging in rote learning, you are likely to forget concepts. So, Hence, c = 3 4 The points are: (-2, 3), ($\frac{4}{5}$, $\frac{13}{5}$) Prove: AB || CD So, m = $\frac{0 + 3}{0 1.5}$ Hence, from the above, -2 3 = c In Exercises 27-30. find the midpoint of $\overline{P Q}$. (7x + 24) = 180 72 y = -3x + b (1) We can conclude that the given statement is not correct. d = $\sqrt{(8 + 3) + (7 + 6)}$ Hence, HOW DO YOU SEE IT? We know that, Prove m||n Substitute A (8, 2) in the above equation Hence, from the above figure, Perpendicular to $5x3y=18$ and passing through $(9, 10)$. Use the diagram -x + 4 = x 3 We can conclude that 44 and 136 are the adjacent angles, b. y y1 = m (x x1) b. m1 + m4 = 180 // Linear pair of angles are supplementary In Exercise 31 on page 161, from the coordinate plane, In Exercises 11 and 12. find m1, m2, and m3. d = 364.5 yards We know that, Hence, from the above, Answer: The coordinates of a quadrilateral are: b.) The given figure is: b is the y-intercept Slope of TQ = $\frac{-3}{-1}$ Since the given line is in slope-intercept form, we can see that its slope is $m=5$. The given equation is: = $1,20,512 The alternate interior angles are: 3 and 5; 2 and 8, c. alternate exterior angles The missing information the student assuming from the diagram is: So, Answer: Answer: -3 = -4 + c Consecutive Interior Angles Converse (Theorem 3.8) Substitute A (2, -1) in the above equation to find the value of c Answer: = $\frac{5}{6}$ The given figure is: Substitute (1, -2) in the above equation Now, Perpendicular lines intersect at each other at right angles Each bar is parallel to the bar directly next to it. The conjecture about $\overline{A O}$ and $\overline{O B}$ is: