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How can you prove that a constructed line is parallel to a given line Assume that the transversal line is not perpendicular to the other lines?
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∙ 11y ago
If the lines have the same slope but with different y intercepts then they are parallel
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∙ 11y ago
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Are railway lines parallel or perpendicular?
Railway lines are parallel. 2 lines are said to be parallel when they are contained in the same plane and do not intersect. This is the definition. That parallel lines exist is an assumption (postulate) of Euclidean geometry:Parallel lines are like the rails of a train track, and you might think of defining them this way, as lines that are the same distance apart everywhere. The problem with this kind of definition is it assumes both tracks are straight. Though this seems an obvious possibility, when you go into the vast universe it is not that obvious. Parallel lines puzzled the best mathematicians for centuries until it was realized that we must assume they exist (you can't prove they exist from simpler postulates). The problem with parallel lines lies in the notion that the lines have infinite extent.Euclid used a somewhat different parallel postulate in trying to avoid the notion of the infinite. He observed that when two parallel lines are intersected by a third line, called a transversal, then if you measure two angles formed by these three lines, on the same side of the transversal and between the parallels, they will add to (that is, they will be supplementary). Such angles are called same-side interior angles.Another important concept is perpendicular. By definition, two lines are perpendicular if they intersect at right angles. That is, two perpendicular lines form 4 right angles. Segments and rays can also be perpendicular. This means they intersect in at least one point, and the two lines containing them are perpendicular.We use perpendicular segments to measure the distance from a point to a line, a point to a plane, or the distance between two parallel lines or planes. The ties of a railroad track are perpendicular to the rails and of the same length. This common length is the distance between the rails. (If parallel lines exist, then railroad tracks in space can go on forever.)There are three theorems about perpendicular lines that you should know. We will not attempt to prove them here, but if you think about them they should be rather obvious.We can use this fact to define the distance from a point to a line: That distance is the length of a segment perpendicular to the line with the given point as one of its endpoints and the other endpoint on the line. In fact, a similar notion holds in 3 dimensions. If we have a plane and a point not on that plane, then there is only one line through the point perpendicular to the plane, and the length of the segment determined by that point and the intersection of the perpendicular line with the plane is defined as the distance from the point to.
Assume you have two lines which are perpendicular If one line has a slope of 3 what is the slope of the other line?
-(1/3)
What equation represents a line that is parallel to the line reprensented by the equation y equals -2 plus 5?
I assume the question should be y = -2x + 5? The equation of a line that is parallel to that line is any line that begins 7 = -2x ... after the -2x any number may be added or subtracted. Parallel lines have the same slope. In the original equation, the slope is -2.
What type of lines are these y 2x 4 and x 2y 12?
Unfortunately, limitations of the browser used by WA means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc. They cannot be parallel and so, since the question has been asked, as is clearly part of your homework, it must have an answer other than "random lines". So then, if you assume that the lines are y = 2x + 4 and x + 2y = 12 they are mutually perpendicular.
What is five less than one fourth the quantity of three times a number plus eight?
(((x*3)/4)+8)-5 = y --------------------------------------------------------------------------------------------------- Assume the number is Y three times the number + 8 = 3Y + 8 1/4 th this quantity is (3Y + 8)/4 then 5 less this quantity = 5 - (3Y + 8)/4 Assume Y = 4 for example then the result is zero Assume Y = 8 for example then the result is -3 Assume Y = zero then the result is +3
How can you prove that a constructed line is parallel to a given line Assume that the transversal line is not perpendicular to the other lines.?
By using a protractor which will show that corresponding angles are equal and alternate angles are equal .
What can and cannot be assumed about a figure?
You can assume only given information and some angle relationships such as vertical angles and linear pairs. You cannot assume any ungiven angle measures or relationships of lines such as parallel or perpendicular.
What is alternate interior angles?
Let be a set of lines in the plane. A line k is transversal of if # , and # for all . Let be transversal to m and n at points A and B, respectively. We say that each of the angles of intersection of and m and of and n has a transversal side in and a non-transversal side not contained in . Definition:An angle of intersection of m and k and one of n and k are alternate interior angles if their transversal sides are opposite directed and intersecting, and if their non-transversal sides lie on opposite sides of . Two of these angles are corresponding angles if their transversal sides have like directions and their non-transversal sides lie on the same side of . Definition: If k and are lines so that , we shall call these lines non-intersecting. We want to reserve the word parallel for later. Theorem 9.1:[Alternate Interior Angle Theorem] If two lines cut by a transversal have a pair of congruent alternate interior angles, then the two lines are non-intersecting.Figure 10.1: Alternate interior anglesProof: Let m and n be two lines cut by the transversal . Let the points of intersection be B and B', respectively. Choose a point A on m on one side of , and choose on the same side of as A. Likewise, choose on the opposite side of from A. Choose on the same side of as C. Hence, it is on the opposite side of from A', by the Plane Separation Axiom. We are given that . Assume that the lines m and n are not non-intersecting; i.e., they have a nonempty intersection. Let us denote this point of intersection by D. D is on one side of , so by changing the labeling, if necessary, we may assume that D lies on the same side of as C and C'. By Congruence Axiom 1 there is a unique point so that . Since, (by Axiom C-2), we may apply the SAS Axiom to prove thatFrom the definition of congruent triangles, it follows that . Now, the supplement of is congruent to the supplement of , by Proposition 8.5. The supplement of is and . Therefore, is congruent to the supplement of . Since the angles share a side, they are themselves supplementary. Thus, and we have shown that or that is more that one point, contradicting Proposition 6.1. Thus, mand n must be non-intersecting. Corollary 1: If m and n are distinct lines both perpendicular to the line , then m and n are non-intersecting. Proof: is the transversal to m and n. The alternate interior angles are right angles. By Proposition 8.14 all right angles are congruent, so the Alternate Interior Angle Theorem applies. m and n are non-intersecting. Corollary 2: If P is a point not on , then the perpendicular dropped from P to is unique. Proof: Assume that m is a perpendicular to through P, intersecting at Q. If n is another perpendicular to through P intersecting at R, then m and n are two distinct lines perpendicular to . By the above corollary, they are non-intersecting, but each contains P. Thus, the second line cannot be distinct, and the perpendicular is unique. The point at which this perpendicular intersects the line , is called the foot of the perpendicular
Are railway lines parallel or perpendicular?
Railway lines are parallel. 2 lines are said to be parallel when they are contained in the same plane and do not intersect. This is the definition. That parallel lines exist is an assumption (postulate) of Euclidean geometry:Parallel lines are like the rails of a train track, and you might think of defining them this way, as lines that are the same distance apart everywhere. The problem with this kind of definition is it assumes both tracks are straight. Though this seems an obvious possibility, when you go into the vast universe it is not that obvious. Parallel lines puzzled the best mathematicians for centuries until it was realized that we must assume they exist (you can't prove they exist from simpler postulates). The problem with parallel lines lies in the notion that the lines have infinite extent.Euclid used a somewhat different parallel postulate in trying to avoid the notion of the infinite. He observed that when two parallel lines are intersected by a third line, called a transversal, then if you measure two angles formed by these three lines, on the same side of the transversal and between the parallels, they will add to (that is, they will be supplementary). Such angles are called same-side interior angles.Another important concept is perpendicular. By definition, two lines are perpendicular if they intersect at right angles. That is, two perpendicular lines form 4 right angles. Segments and rays can also be perpendicular. This means they intersect in at least one point, and the two lines containing them are perpendicular.We use perpendicular segments to measure the distance from a point to a line, a point to a plane, or the distance between two parallel lines or planes. The ties of a railroad track are perpendicular to the rails and of the same length. This common length is the distance between the rails. (If parallel lines exist, then railroad tracks in space can go on forever.)There are three theorems about perpendicular lines that you should know. We will not attempt to prove them here, but if you think about them they should be rather obvious.We can use this fact to define the distance from a point to a line: That distance is the length of a segment perpendicular to the line with the given point as one of its endpoints and the other endpoint on the line. In fact, a similar notion holds in 3 dimensions. If we have a plane and a point not on that plane, then there is only one line through the point perpendicular to the plane, and the length of the segment determined by that point and the intersection of the perpendicular line with the plane is defined as the distance from the point to.
Parallel lines are equidistant and will never meet?
I understand your question to be, "Is it true that parallel lines are everywhere equidistant and never intersect?" In what follows, I assume we're talking about a two-dimensional plane. By definition, two lines that are parallel (in the same plane) never intersect. In Euclidean (AKA Parabolic or simply E) Geometry, and also in Hyperbolic (AKA simply L) Geometry, parallel lines exist. In Elliptical (AKA R) Geometry, all lines eventually intersect so parallel lines do not exist. Now, are two parallel lines (in the same plane) everywhere equidistant? If so, that means that it is possible, at any point on one of the lines, to construct a perpendicular that will meet the other line in a perpendicular, and that the length of the segments constructed will be always the same. In Euclidean Geometry, two parallel lines (in a plane) are indeed everywhere equidistant. To prove it requires the converse of the Alternate Interior Angles theorem (AIA), which says that if two parallel lines are cut by a transversal, the alternate interior angles will be congruent. Note that this is the CONVERSE of AIA, not AIA. Some people get this mixed up. In Hyperbolic Geometry, two lines can be parallel, but be further apart some places than others. I know that sounds rather odd, if you're not used to it. Here's an image that might help: imagine that your plane is a thin sheet of rubber, and for some reason is being stretched. The further you go from your starting point, the more it stretches, and it's always stretching away from you. This means that your parallel lines will keep getting further and further apart.
Let v and a represent the velocity and accelerationrespestivelyof an automobileDescribe circumstances in whichv and a are parallelv and a are antiparallelv and a are perpendicular to one another?
When they are parallel, the automobile has a positive acceleration (it is speeding up). When they are antiparallel (I assume you mean at 180 degrees to each other but in the opposite direction), the automobile has a negative acceleration (it is slowing down). When they are perpendicular they have no effect on each other, therefore the car has a constant velocity.
How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
Assume you have two lines which are perpendicular If one line has a slope of 3 what is the slope of the other line?
-(1/3)
Does the letter G have parallel lines?
No, the letter G does not have any parallel lines, but there are a few ways of looking at it. If you assume the arc of the letter (the part that makes the shape of a C) as one line, then the letter G doesn't have any parallel lines. But... If you assume the arc as to being a lot of individual lines, and NOT an arc, then it is likely that the letter G does have a parallel line or two.
Do parrallel lines meet?
Not in Euclidean Geometry. Euclid's 5th axiom is that parallel lines never meet. However, unlike the first 4 axiom, it is impossible to prove the 5th axiom; depending upon the situation, you can either assume that parallel lines meet or don't; when they do meet, there are some very interesting consequences (for example, the possibility of a hyperbolic space). To my knowledge, if they meet, they are intersecting/perpendicular lines.
When was the statue of zeus constructed?
i dont know which one you mean but ill assume the one in olympia which was built around 432b.c.
What is the same-side interior angles postulate?
Technically this does not exist. Many math texts use it as a shortcut to introduce properties of angles for parallel lines that are cut by a transversal. It says that when lines are parallel and are cut by a transversal, then the same side interior angles must be supplementary (add up 180 degrees). Once you say this is a postulate (assumed to be true), then you can prove other things like the Congruent Corresponding Angles theorem that says "If lines are parallel and are cut by a transversal, then the corresponding angles must be conguent." Some texts do the reverse and say Corresponding Angles is a postulate and then prove Same-Side Interior as a Theorem. Euclid proved both these using his 5th Postulate (often re-written as the Parallel Postulate or Playfair's Axiom). To do this, he had to prove that the interior angles of a triangle sum to 180. Since many Math Texts do not introduce this fact until later chapters, they take this shortcut of "assume the Same-Side Interior" is true and the remaining theorems are much easier. Another reason Math books may take this shortcut is that Euclid's method is usually done by proof by contradiction - which is sometimes more difficult to understand. I believe the Khan Academy video of this material is done correctly.
