In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us. In the figure below, line “AB” is parallel to the line “CD”. The perpendicular distance is always the same between two parallel lines. Sides of various shapes are parallel to each other. In the rectangle given below, the single arrow lines are parallel to each other, and similarly, the double arrow lines are also parallel to each other. Parallel lines are represented with a pair of vertical lines between the names of the lines, using the sign: ︳︳ Draw parallel lines on a sheet, Use a ruler to make them neat! Make sure their ends never meet! A transversal is a line that intersects two parallel lines (or lines on a plane) at different intersecting points, forming angles. Parallel lines can
be easily identified using the following fundamental properties and characteristics: Linear equations are generally described by the slope-intercept represented by the equation $y = mx + b$. Where “m” is the slope, “b” is the y-intercept, and y and x are variables. The value of “m” determines the slope and indicates the steep slope of the line. Note that the slopes of the two parallel lines are always the same. For example, if the slope of the straight line in the equation y $= 4x + 3$ is 4, then all lines parallel to $y = 4x + 3$ have the same slope, or 4. Parallel lines have different y-intersections and have no points or angles in common. Solved ExamplesExample 1: Find out which lines are parallel to each other in the given figure. Solution: All the three lines with arrows passing through them are parallel to each other, which means: a || b || c Lines with the double arrows, i.e., line d and e are transversals of lines a, b, and c, but they are parallel to each other. So, we can say that d || e Example 2: Find whether the given lines intersected by a transversal in the figure are parallel or not. Solution: The two lines are parallel as they meet one of the properties of parallel lines “when the alternate interior angles are equal, the lines are parallel”. $∠a$ is equal to $∠c$, and both of these are alternate interior angles. This proves that the two lines are parallel. Example 3: Are the lines intersected by the transversal in this figure parallel? Solution: According to the given properties of parallel lines, the alternating, corresponding, and consecutive angles should be the same to form parallel lines. In this case, $∠a$ is not equal to $∠d $ Thus, these two lines are not parallel. Practice ProblemsNoncoplanar Coplanar Equidistant Lines running in the same direction Correct answer is:
Noncoplanar Clock hands Wipers of a car Stairs and railings Strings of a tennis racket net Correct answer is: Clock hands $120°$ $0°$ $112°$ $224°$ Correct answer is: $112°$ Frequently Asked QuestionsWhat are the different types of parallel lines? Parallel lines can be vertical, diagonal, and horizontal. How are parallel lines used in coordinate geometry? If the graphs of two linear equations of coordinate geometry are parallel, then the two equations have no common solution. The slopes of two parallel lines are the same and always equal in coordinate geometry. How can you prove that two lines are parallel? You can use some geometric relationships to prove that two lines are parallel. A transversal is a line that intersects two or more lines. When a line intersects a pair of parallel lines, a pair of different angles are formed. These different types of angles are used to prove whether the two lines are parallel to each other according to the given properties of parallel lines. Which of the following is the photosynthetic stage that produces oxygen *?Photosynthesis occurs in two stages. During the first stage, the energy from sunlight is absorbed by the chloroplast. Water is used, and oxygen is produced during this part of the process. During the second stage, carbon dioxide is used, and glucose is produced.
Which of the following reactions occur in both cellular respiration and photosynthesis?Which process occurs in both cellular respiration and photosynthesis? Explanation: In both cellular respiration and photosynthesis, chemiosmosis occurs. Chemiosmosis is the process in which the creation of a proton gradient leads to the transport of proton down its concentration gradient to produce ATP.
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