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From Encyclopedia

Lines, Parallel and Perpendicular Lines, Parallel and Perpendicular

In mathematics, the term "straight line" is one of the few terms that is left undefined. However, most people are comfortable with this undefined concept, which can be modeled by a pencil, a stiff wire, the edge of a ruler, or even an uncooked piece of spaghetti. Mathematicians sometimes think of a line as a point moving forever through space. Lines can be curved or straight, but in this entry, only straight lines are considered. A line, in the language of mathematics, has only one dimension—length—and has no end. It stretches on forever in both directions, so that its length cannot be measured. When a line is modeled with a piece of spaghetti, a line segment is actually being represented. The model of a line segment has thickness (or width), while the idea that it models—a mathematical line—does not. So a mathematical line is a notion in one's mind, rather than a real object one can touch and feel, just as the notion of "two" is an idea in one's mind—that quality and meaning that is shared by two apples, two trucks, and the symbols //, 2, ☺☺, and ii. Think of two straight lines in a plane (another undefined term in geometry ). Someone can model this idea, imperfectly, by two pencils or two pieces of spaghetti lying on a desktop. Now, mentally or on a desktop, push these lines around, still keeping them on the plane, and see the different ways two lines can be arranged. If these two lines meet or cross, they have one point in common. In the language of mathematics, the two lines intersect at one point, their point of intersection. If two lines are moved so that they coincide, or become one line, then they have all of their points in common. What other arrangements are possible for two lines in a plane? One can place them so that they do not coincide (that is, one can see that they are two separate lines), and yet they do not cross, and will never cross, no matter how far they are extended. Two lines in the same plane, which have no point in common and will never meet, are called parallel lines. If one draws a grid, or coordinate system, on the plane, she can see that two parallel lines have the same slope, or steepness. Are there any parallel lines in nature, or in the human-made world? There are many models of parallel lines in the world we build: railroad tracks, the opposite sides of a picture frame, the lines at the corners of a room, fence posts. In nature, parallel lines are not quite so common, and the models are only approximate: tracks of an animal in the snow, tree trunks in a forest, rays of sunlight. The only other possible arrangement for two lines in the plane is also modeled by a picture frame, or a piece of poster board. Two sides of a rectangle that are not parallel are perpendicular . Perpendicular lines meet, or intersect, at right angles, that is, the four angles formed are all equal. The first pair of lines in part (a) of the figure below meet to form four equal angles; they are perpendicular. The second pair in part (b) forms two larger angles and two smaller ones; they are not perpendicular. Perpendicular lines occur everywhere in buildings and in other constructions. Like parallel lines, they are less common in nature. On a coordinate system, two perpendicular lines (unless one of them is horizontal) have slopes that multiply to a product of -1; for example, if a line has a slope of 3, any line perpendicular to it will have a slope of -⅓. see also Lines, Skew; Slope. Lucia McKay Anderson, Raymond W. Romping Through Mathematics. New York: Alfred A. Knopf, 1961. Juster, Norton. The Dot and the Line: A Romance in Lower Mathematics. New York: Random House, 1963. Konkle, Gail S. Shapes and Perception: An Intuitive Approach to Geometry. Boston: Prindle, Weber and Schmidt, Inc., 1974.


From Yahoo Answers

Question:Parallel lines with a non-perpendicular transversal Complementary adjacent angles formed by two intersecting lines Concentric triangles with parallel edges Internally tangent circles Trapezoid with two right angles 3-4-5 triangle Two non-perpendicular bisecting line segments andand.. is a star a concave polygon? O_o Also, is pacman a good example of a major arc not part of a full circle? Thank you!

Answers:If you weld bars of metal together in lines. I think a star is a concave polygon. Yes pacman is a good example

Question:I have to take pictures of things in everyday life that represent these geometry subjects. They are: Acute Angle Adjacent Angle Angle Bisector Collinear Concave Polygon Congruent Convex Polygon Line Line Segment Linear pair Midpoint Obtuse Angle Parallel lines Perpendicular Lines Plane Point Ray Right Angle Slope Vertical Angles If you could help me by giving examples of what in the real world could represent any of these, that would be great. I have a couple but I just want to make sure that I am good on them. Thank you. =]

Answers:Acute Angle : find something triangular. All triangles have at least one acute angle Adjacent Angle : take that same triangular thing and any 2 angles are adjacent. Angle Bisector : Collinear find something with a straight line and any 3 (or more) things along that line are collinear Concave Polygon Congruent: get two things that are identical in size Convex Polygon Line : use a yardstick and mention it goes on forever. Route 66 goes across the country, but it is not straight Line Segment : use a ruler Linear pair Midpoint: the number 6 on a ruler Obtuse Angle; get a triangle again Parallel lines; find a box and two of the edges will be parallel Perpendicular Lines ; use the same box and use two edges that are perpendicular Plane ; a piece of paper could represent a plane surface, understand it goes on in all directions Point; has no dimensions, but for school purposes, a dot Ray: the graph of the absolute value of x Right Angle: anything that meets at a right angle. Use the box again Slope: a hill Vertical Angles: a map where 2 roads cross good luck

Question:Could you give me some ideas on how these examples of geometry terms are represented in real life? It is supposed to be objects. Here are the terms. Point Line Segment Ray Opposite Rays Perpendicular Lines Parrallel Lines Acute Angle Obtuse Angle Right Angle Vertical Angles (Acute only) Adjacent Angles (must be less than 180 Degrees) Linear Pair Thank you so much !

Answers:You have to put down tile or some type of flooring, you need to be able to use these to figure out how much tile to order and then how to lay this tile so that you have to cut the least amount (I mean really who wants to cut tiles for forever).

Question:I need to find five real world examples for these angles and lines: an acute angle a right angle an obtuse angle vertical angles adjacent angles parallel lines (or line segments) perpendicular lines (or line segments) intersecting lines (or line segments) a transversal intersecting a set of parallel lines corresponding angles You dont have to find five for all of them, just one or two would be ok, and i could think of the rest. Thanks

Answers:look on street corners, the sides of buildings, railings, etc. if you really look around you'll find you're surrounded by angles and lines.

From Youtube

Perpendicular Bisector of a Line :Tutorial on how to write the perpendicular bisector of a line segment. Demo lesson followed by two example problems worked out step by step. Watch video to see how you can also get a free worksheet on perpendicular bisectors

Perpendicular to a Vertical Line :This video illustrates how to find the equation of a line that passes through a given point, and is perpendicular to a vertical line whose equation is given. For part 2 of this video, including example 2, as well as many more instructuional Math videos with exercise and answer sheets, go to: www.thefreemathtutor.com