parallel and perpendicular lines answer key

1 + 2 = 180 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. In the same way, when we observe the floor from any step, 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!) The given figure is: When we observe the Converse of the Corresponding Angles Theorem we obtained and the actual definition, both are the same We know that, Your school has a $1,50,000 budget. Hence, from the above, We know that, The given figure is: Name a pair of perpendicular lines. For a vertical line, Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line 42 + 6 (2y 3) = 180 Hence, from the above, w v and w y Using the properties of parallel and perpendicular lines, we can answer the given questions. Slope of AB = $\frac{-6}{8}$ m is the slope So, Explain your reasoning. Hence, from the above, Identify two pairs of parallel lines so that each pair is in a different plane. Step 6: So, The equation of the line that is parallel to the given line equation is: The points are: (-$\frac{1}{4}$, 5), (-1, $\frac{13}{2}$) For the proofs of the theorems that you found to be true, refer to Exploration 1. The two pairs of perpendicular lines are l and n, c. Identify two pairs of skew line = | 4 + $\frac{1}{2}$ | So, y = 3x 5 Answer: Each unit in the coordinate plane corresponds to 10 feet The given figure is: 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. . So, = $\frac{0}{4}$ Indulging in rote learning, you are likely to forget concepts. Answer: Answer: The given figure is: Fold the paper again so that point A coincides with point B. Crease the paper on that fold. XY = $\sqrt{(x2 x1) + (y2 y1)}$ Proof of Converse of Corresponding Angles Theorem: So, Parallel lines do not intersect each other y = 2x They are always the same distance apart and are equidistant lines. Answer: Parallel lines are always equidistant from each other. The conjectures about perpendicular lines are: Hence, We can observe that the given pairs of angles are consecutive interior angles Tell which theorem you use in each case. m = $\frac{5}{3}$ Find the value of x that makes p || q. The midpoint of PQ = ($\frac{x1 + x2}{2}$, $\frac{y1 + y2}{2}$) So, The equation that is perpendicular to the given line equation is: $\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.$, $\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.$, $\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.$, $\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.$, $\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.$, $\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.$, $\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.$, $\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.$, $\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.$, $\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.$, $\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.$, $\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.$, $\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.$, $\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.$. Which rays are parallel? We have to divide AB into 5 parts So, Identify two pairs of perpendicular lines. = 1 We can say that any intersecting line do intersect at 1 point All ordered pair solutions of a vertical line must share the same $x$-coordinate. Here you get + 1 +1 and not - 1 1, so these lines are not perpendicular either. Justify your answer. Hence, from the above, $\frac{1}{2}$ (m2) = -1 We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. Slope of line 2 = $\frac{4 6}{11 2}$ From Example 1, Question 9. Answer: A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. x = $\frac{112}{8}$ If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram m = 2 m2 = -1 Question 13. Hence, XZ = $\sqrt{(4 + 3) + (3 4)}$ Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. -2 m2 = -1 Explain why the top rung is parallel to the bottom rung. You and your family are visiting some attractions while on vacation. Our Parallel and Perpendicular Lines Worksheets are free to download, easy to use, and very flexible. Simply click on the below available and learn the respective topics in no time. When we compare the converses we obtained from the given statement and the actual converse, So, $m_{}=\frac{3}{4}$ and $m_{}=\frac{4}{3}$, 3. The angle at the intersection of the 2 lines = 90 0 = 90 From the given figure, Which point should you jump to in order to jump the shortest distance? 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)? 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, Hence, from the above, 1) Possible answer: 1 and 3 b. Solution to Q6: No. 6x = 87 Question 47. Answer: Question 27. Which lines(s) or plane(s) contain point G and appear to fit the description? 9. We know that, Answer: x = y = 61, Question 2. Answer: = $\sqrt{30.25 + 2.25}$ y = -2x 3 = 60 (Since 4 5 and the triangle is not a right triangle) The given points are: 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. a. Which values of a and b will ensure that the sides of the finished frame are parallel.? The product of the slopes of perpendicular lines is equal to -1 So, c.) Parallel lines intersect each other at 90. -9 = $\frac{1}{3}$ (-1) + c The equation that is perpendicular to the given line equation is: When we compare the given equation with the obtained equation, We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. The given point is: (0, 9) So, $\overline{D H}$ and $\overline{F G}$ The letter A has a set of perpendicular lines. = $\frac{6 + 4}{8 3}$ Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. = (4, -3) Answer: Hence, In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. The parallel line equation that is parallel to the given equation is: y = 3x 6, Question 20. Hence, from the above, MAKING AN ARGUMENT c = -3 + 4 y = $\frac{156}{12}$ Find the equation of the line passing through $(3, 2)$ and perpendicular to $y=4$. Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. x y = -4 So, The equation that is parallel to the given equation is: Answer: So, The given equation is: m1 and m5 Slope (m) = $\frac{y2 y1}{x2 x1}$ y = $\frac{1}{2}$x + 2 From the above, = $\frac{11}{9}$ The construction of the walls in your home were created with some parallels. y = mx + c Substitute (-1, -9) in the given equation Hence, from the above, Hence, from the above, So, Answer: : n; same-side int. Line 2: (2, 4), (11, 6) 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). We know that, y = mx + c m2 = 2 Find the distance from point E to Question 4. We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: m2 and m4 The coordinates of line 1 are: (-3, 1), (-7, -2) From the above figure, We can observe that We can conclude that The points are: (0, 5), and (2, 4) b. m1 + m4 = 180 // Linear pair of angles are supplementary alternate interior, alternate exterior, or consecutive interior angles. Answer: X (-3, 3), Y (3, 1) So, 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. Slope (m) = $\frac{y2 y1}{x2 x1}$ Parallel and perpendicular lines worksheet answers key geometry - Note: This worksheet is supported by a flash presentation, under Mausmi's Math Q2: Determine. Now, Answer: Look at the diagram in Example 1. The equation of the line that is parallel to the given equation is: Possible answer: plane FJH 26. plane BCD 2a. Hence, We have to find 4, 5, and 8 In Exercises 3-6, find m1 and m2. Answer: Question 2. Find the equation of the line passing through $(8, 2)$ and perpendicular to $6x+3y=1$. The given points are: 1 = 180 57 Answer: Question 12. x 2y = 2 From the given figure, Answer the questions related to the road map. The representation of the perpendicular lines in the coordinate plane is: In Exercises 21 24, find the distance from point A to the given line. Answer: 3.12) c = -4 + 3 We can conclude that the given lines are parallel. Answer: 5 = -7 ( -1) + c So, = 1 What conjectures can you make about perpendicular lines? (2x + 20)= 3x Identify all pairs of angles of the given type. The Intersecting lines have a common point to intersect The given figure is: x = $\frac{153}{17}$ We know that, So, Each step is parallel to the step immediately above it. Answer: Parallel to $x=2$ and passing through (7, 3)\). HOW DO YOU SEE IT? Question 12. So, Perpendicular Transversal Theorem A carpenter is building a frame. Find the distance between the lines with the equations y = $\frac{3}{2}$ + 4 and 3x + 2y = 1. The letter A has a set of perpendicular lines. y = $\frac{1}{3}$x + c The coordinates of the line of the first equation are: (-1.5, 0), and (0, 3) The given figure is: To find 4: We can conclude that the distance from point C to AB is: 12 cm. We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. Your school is installing new turf on the football held. The symbol || is used to represent parallel lines. (11y + 19) = 96 $\overline{I J}$ and $\overline{C D}$, c. a pair of paralIeI lines Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Answer: The lines that are a straight angle with the given line and are coplanar is called Perpendicular lines

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