parallel and perpendicular lines answer key

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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. Consider the following two lines: Consider their corresponding graphs: Figure 4.6.1 Question 14. = $\frac{3}{4}$ Answer: Then, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1. d = $\sqrt{(x2 x1) + (y2 y1)}$ The slope of the given line is: m = 4 Although parallel and perpendicular lines are the two basic and most commonly used lines in geometry, they are quite different from each other. Answer: In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning. The representation of the Converse of Corresponding Angles Theorem is: b. Alternate Interior Angles Theorem (Theorem 3.2): If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Question 27. P(2, 3), y 4 = 2(x + 3) We can conclude that the pair of parallel lines are: So, We can conclude that the distance from point A to $\overline{X Z}$ is: 4.60. Hence, from the above, So, Hence, from the above, Hence, from the above, Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent Answer: Answer: y = $\frac{2}{3}$x + b (1) 2 + 3 = 180 consecutive interior We can conclude that the distance from line l to point X is: 6.32. $\overline{I J}$ and $\overline{C D}$, c. a pair of paralIeI lines The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. Perpendicular lines are denoted by the symbol . The given figure is: Question 1. From the above figure, If p and q are the parallel lines, then r and s are the transversals Question 39. x = $\frac{153}{17}$ 48 + y = 180 Answer: P(0, 1), y = 2x + 3 ATTENDING TO PRECISION Answer: Answer: Question 14. Slope of JK = $\frac{n 0}{0 0}$ Hence, So, From the figure, x = $\frac{120}{2}$ Answer: The given point is: A (-1, 5) The equation for another line is: We can conclude that $\overline{P R}$ and $\overline{P O}$ are not perpendicular lines. y 175 = $\frac{1}{3}$ (x -50) 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 Question 1. m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem The equation of the line that is parallel to the given line equation is: Select the orange Get Form button to start editing. It is given that m || n One way to build stairs is to attach triangular blocks to angled support, as shown. The slope of one line is the negative reciprocal of the other line. Answer: 1 = 2 = 123, Question 11. The parallel line equation that is parallel to the given equation is: Homework 1 - State whether the given pair of lines are parallel. d = $\sqrt{(11) + (13)}$ The sum of the angle measure between 2 consecutive interior angles is: 180 You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks. Answer: Answer: Answer: So, y = mx + b Hence, from the above, So, So, CRITICAL THINKING (50, 175), (500, 325) From the given figure, From the given figure, c = $\frac{26}{3}$ (7x + 24) = 180 72 Using the same compass selling, draw an arc with center B on each side $\overline{A B}$. Hence, from the above, Answer: Question 31. (B) intersect We know that, Substitute A (0, 3) in the above equation a. (1) = Eq. Explain why ABC is a straight angle. It is given that Substitute P (4, 0) in the above equation to find the value of c The given point is: A (3, 4) The area of the field = Length Width So, Hence, Compare the given coordinates with (x1, y1), and (x2, y2) 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. y = $\frac{1}{2}$x + 2 The representation of the given pair of lines in the coordinate plane is: y = mx + b b. PROVING A THEOREM Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. So, y = mx + c Hence, from the above, Substitute A (-6, 5) in the above equation to find the value of c So, Now, Will the opening of the box be more steep or less steep? it is given that the turf costs $2.69 per square foot Yes, I support my friends claim, Explanation: So, We know that, y = mx + c It is given that Hence, y = 2x y = mx + c PROBLEM-SOLVING y = $\frac{3}{2}$ + 4 and y = $\frac{3}{2}$x $\frac{1}{2}$ Hence, from the above, The given figure is: The equation of the line that is perpendicular to the given equation is: = (4, -3) The distance between the perpendicular points is the shortest So, We know that, 11y = 77 2y + 4x = 180 You and your friend walk to school together every day. The given equation is: The equation of the line along with y-intercept is: The given point is: (3, 4) The equation that is parallel to the given equation is: She says one is higher than the other. Hence, from the above figure, If it is warm outside, then we will go to the park A(- 3, 2), B(5, 4); 2 to 6 So, Now, Hence, from the above, Horizontal and vertical lines are perpendicular to each other. Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. Now, -3 = -2 (2) + c The product of the slopes of the perpendicular lines is equal to -1 For a square, In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. -1 = 2 + c We can conclude that the converse we obtained from the given statement is true The equation of a line is: Hence, A(- 6, 5), y = $\frac{1}{2}$x 7 So, y = $\frac{1}{3}$x 4 alternate interior Where, 1. Answer: Answer: y = -x + 8 We know that, FSE = ESR Justify your conclusion. 5x = 132 + 17 In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. We can conclude that These worksheets will produce 6 problems per page. So, X (-3, 3), Y (3, 1) How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? Now, In Exercises 15 and 16, use the diagram to write a proof of the statement. The coordinates of line a are: (0, 2), and (-2, -2) Work with a partner: Write the converse of each conditional statement. We can observe that the slopes are the same and the y-intercepts are different The letter A has a set of perpendicular lines. Slope of AB = $\frac{1 + 4}{6 + 2}$ Find the distance between the lines with the equations y = $\frac{3}{2}$ + 4 and 3x + 2y = 1. The slope of the line of the first equation is: The given points are: P (-7, 0), Q (1, 8) $\overline{C D}$ and $\overline{E F}$, d. a pair of congruent corresponding angles Prove 1 and 2 are complementary We know that, Now, Example 2: State true or false using the properties of parallel and perpendicular lines. The diagram that represents the figure that it can not be proven that any lines are parallel is: So, Find m1. The product of the slopes of the perpendicular lines is equal to -1 Look at the diagram in Example 1. Furthermore, the rise and run between two perpendicular lines are interchanged. 5 + 4 = b The distance between lines c and d is y meters. V = (-2, 3) Answer: The sides of the angled support are parallel. Step 4: 2 and 3 are the consecutive interior angles It is not always the case that the given line is in slope-intercept form. Since it must pass through $(3, 2)$, we conclude that $x=3$ is the equation. c = -2 7 = -3 (-3) + c Transitive Property of Parallel Lines Theorem (Theorem 3.9),/+: If two lines are parallel to the same line, then they are parallel to each other. Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. y = 2x + 7. d. AB||CD // Converse of the Corresponding Angles Theorem = $\frac{1}{-4}$ b = -7 2x + y + 18 = 180 y = $\frac{3}{2}$x + 2 = $\frac{-3}{4}$ We can conclude that 4 and 5 angle-pair do not belong with the other three, Monitoring Progress and Modeling with Mathematics. (B) Alternate Interior Angles Converse (Thm 3.6) c = 5 3 Answer: what Given and Prove statements would you use? Answer: The line parallel to $\overline{Q R}$ is: $\overline {L M}$, Question 3. 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 given equation is: The line that is perpendicular to y=n is: Hence, from the above, Answer Keys - These are for all the unlocked materials above. Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines The given points are: For example, AB || CD means line AB is parallel to line CD. So, Answer: Slope of the line (m) = $\frac{y2 y1}{x2 x1}$ Answer: Question 20. The Coincident lines may be intersecting or parallel $\frac{1}{2}$ (m2) = -1 d = $\sqrt{(x2 x1) + (y2 y1)}$ Compare the given equation with Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. The given coordinates are: A (-3, 2), and B (5, -4) To find the distance from point A to $\overline{X Z}$, Now, We know that, Proof of the Converse of the Consecutive Interior angles Theorem: We know that, The resultant diagram is: The slope of the given line is: m = $\frac{1}{2}$ 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. 2 = 140 (By using the Vertical angles theorem) To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles Hence,f rom the above, c = $\frac{9}{2}$ It is given that your school has a budget of $1,50,000 but we only need $1,20,512 We can conclude that b = 9 The line parallel to $\overline{E F}$ is: $\overline{D H}$, Question 2. 42 and (8x + 2) are the vertical angles Compare the given points with 12. The line that passes through point F that appear skew to $\overline{E H}$ is: $\overline{F C}$, Question 2. The equation of the line that is parallel to the given equation is: It is given that a student claimed that j K, j l 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. So, b. Hence, from the above, So, The plane containing the floor of the treehouse is parallel to the ground. The given coordinates are: A (-2, 1), and B (4, 5) Some examples follow. To be proficient in math, you need to communicate precisely with others. According to Corresponding Angles Theorem, Respond to your classmates argument by justifying your original answer. Parallel to $7x5y=35$ and passing through $(2, 3)$. The angles that have the common side are called Adjacent angles 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. Answer: y = (5x 17) MATHEMATICAL CONNECTIONS We have to prove that m || n Slope (m) = $\frac{y2 y1}{x2 x1}$ c = 3 We know that, From the converse of the Consecutive Interior angles Theorem, forming a straight line. Hence, from the above, By comparing the given pair of lines with Answer: 5y = 116 + 21 $\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}$. All the Questions prevailing here in Big Ideas Math Geometry Answers Chapter 3 adhere and meets the Common Core Curriculum Standards. According to Perpendicular Transversal Theorem, x = y = 29, Question 8. Substitute A (-9, -3) in the above equation to find the value of c By using the parallel lines property, They are always the same distance apart and are equidistant lines. Answer: The points are: (-$\frac{1}{4}$, 5), (-1, $\frac{13}{2}$) From the given figure, We know that, COMPLETE THE SENTENCE We can conclude that the slope of the given line is: 3, Question 3. So, So, Lines that are parallel to each other will never intersect. From the given figure, So, Line 2: (2, 1), (8, 4) So, How do you know that the lines x = 4 and y = 2 are perpendiculars? 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. Explain. The given figure is: Explain your reasoning. We know that, c. All the lines containing the balusters. So, It is given that We know that, We can conclude that both converses are the same y = mx + c m1 = $\frac{1}{2}$, b1 = 1 We can observe that 2 = 122 Hence those two lines are called as parallel lines. It is given that the given angles are the alternate exterior angles 4 = 2 (3) + c To find the value of c, (1) y = $\frac{1}{2}$x + 6 Let the congruent angle be P Is your friend correct? We can conclude that there are not any parallel lines in the given figure. Answer: We can conclude that the given pair of lines are coincident lines, Question 3. Which of the following is true when are skew? For parallel lines, c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem. (C) are perpendicular Now, The lines that have the same slope and different y-intercepts are Parallel lines The equation that is perpendicular to the given line equation is: The given figure is: We can conclude that the value of the given expression is: $\frac{11}{9}$. From the given bars, Answer: We can observe that Slope of KL = $\frac{n n}{n 0}$ We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. The given lines are the parallel lines y = mx + b Now, Question 43. The given line has the slope $m=\frac{1}{7}$, and so $m_{}=\frac{1}{7}$. These worksheets will produce 6 problems per page. Proof of Alternate exterior angles Theorem: d. AB||CD // Converse of the Corresponding Angles Theorem The slope of line l is greater than 0 and less than 1. So, Statement of consecutive Interior angles theorem: The coordinates of line 1 are: (10, 5), (-8, 9) Hence, from the above, c = 2 1 Let the two parallel lines that are parallel to the same line be G We can conclude that y = $\frac{1}{2}$x + 5 Answer: Question 24. The general steps for finding the equation of a line are outlined in the following example. ERROR ANALYSIS Now, Find the equation of the line passing through $(1, 5)$ and perpendicular to $y=\frac{1}{4}x+2$. So, From the given figure, Answer: We know that, m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem P(- 5, 5), Q(3, 3) To prove: l || k. Question 4. EG = $\sqrt{50}$ y = $\frac{5}{3}$x + c P(- 8, 0), 3x 5y = 6 Answer: Question 2. Substitute (-1, 6) in the above equation Now, The given figure is: ANALYZING RELATIONSHIPS The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, The representation of the given coordinate plane along with parallel lines is: Answer: 2x y = 18 Answer: Question 20. Hence, from the above, Answer: So, Answer: m is the slope b.) 2x y = 4 Slope of line 2 = $\frac{4 + 1}{8 2}$ From the given figure, The equation that is perpendicular to the given line equation is: c. m5=m1 // (1), (2), transitive property of equality So, 5y = 137 ABSTRACT REASONING Hence, from the above, So, x = 107 Hence, from the above, Is there enough information in the diagram to conclude that m || n? Step 6: From the given figure, Answer: Slope of line 1 = $\frac{-2 1}{-7 + 3}$ -3 = -4 + c Justify your conjecture. y = x $\frac{28}{5}$ = $\frac{8}{8}$ Answer: We can observe that the given angles are the corresponding angles 10) y = $\frac{2}{3}$x + c Two lines are cut by a transversal. From the given diagram, Question 13. So, Indulging in rote learning, you are likely to forget concepts. We know that, Using P as the center, draw two arcs intersecting with line m. We can conclude that $\overline{N P}$ and $\overline{P O}$ are perpendicular lines, Question 10. m2 = 1 Because j K, j l What missing information is the student assuming from the diagram? 4 and 5 Question 20. A triangle has vertices L(0, 6), M(5, 8). a) Parallel to the given line: For parallel lines, we cant say anything Using a compass setting greater than half of AB, draw two arcs using A and B as centers The slopes of the parallel lines are the same The given point is: (6, 1) We can observe that 1 and 2 are the alternate exterior angles Hence, from the above, c = $\frac{37}{5}$ Step 5: Answer: A (-3, -2), and B (1, -2) Hence, from the above, -2 = 3 (1) + c We can say that they are also parallel x = 12 Answer: Now, m = = So, slope of the given line is Question 2. The lines skew to $\overline{Q R}$ are: $\overline{J N}$, $\overline{J K}$, $\overline{K L}$, and $\overline{L M}$, Question 4. 9. Justify your answer with a diagram. It is given that 4 5. Find m1 and m2. So, y = 2x 2. Answer: We can observe that when r || s, Answer: No, your friend is not correct, Explanation: We know that, Through the point $(6, 1)$ we found a parallel line, $y=\frac{1}{2}x4$, shown dashed. List all possible correct answers. We can observe that the given angles are corresponding angles y = $\frac{1}{2}$x + c d = $\sqrt{(13 9) + (1 + 4)}$ The given figure is: The product of the slopes of the perpendicular lines is equal to -1 Answer: $\frac{1}{2}$ . Which type of line segment requires less paint? Determine whether the converse is true. From the given figure, Find the equation of the line passing through $(6, 1)$ and parallel to $y=\frac{1}{2}x+2$. So, So, Answer: Each step is parallel to the step immediately above it. Substitute the given point in eq. = 2 (2) What is the distance between the lines y = 2x and y = 2x + 5? The lines that do not intersect or not parallel and non-coplanar are called Skew lines x = 14 The given figure is: HOW DO YOU SEE IT? We know that, When we observe the Converse of the Corresponding Angles Theorem we obtained and the actual definition, both are the same The given figure is: If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. When we compare the given equation with the obtained equation, Substitute (2, -3) in the above equation We know that, So, 1 5 We can conclude that = $\frac{-4 2}{0 2}$ We know that, We know that, Answer: 2 + 10 = c Question 13. Parallel to $y=3$ and passing through $(2, 4)$. Now, The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument You can find the distance between any two parallel lines What flaw(s) exist in the argument(s)? Write the converse of the conditional statement. Hence, The y-intercept is: 9. Question 37. From the given figure, Find the distance from the point (6, 4) to the line y = x + 4. Hence, Hence, They are not parallel because they are intersecting each other. The equation that is parallel to the given equation is: -4 = 1 + b Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. The slope of perpendicular lines is: -1 Hence, The coordinates of P are (3.9, 7.6), Question 3. 5 = -7 ( -1) + c .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.

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