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How many perpendicular lines does a star have?
A geometrical star can have various numbers of vertices, and the angles formed at the vertices need not be the same. The number of perpendicular lines depends on exactly how many vertices it has and how their angles are configured.
Lines on a hyperbolic plane are considered to be?
Hyperbolic geometry is a beautiful example of non-Euclidean geometry. One feature of Euclidean geometry is the parallel postulate. This says that give a line and a point not on that line, there is exactly one line going through the point which is parallel to the line. (That is to say, that does NOT intersect the line) This does not hold in the hyperbolic plane where we can have many lines through a point parallel to a line. But then we must wonder, what do lines look like in the hyperbolic plane? Lines in the hyperbolic plane will either appear as lines perpendicular to the edge of the half-plane or as circles whose centers lie on the edge of the half-plane
What is a another way to say fourth?
something along the lines of quadruple
What is a counterexample of All rectangles have two lines of symmetry?
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
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
What is the definition of a slope of parallel lines?
Horizontal lines have a slope of zero, and the slope of vertical lines is undefined. Parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals of each other. So we can say that: Two nonvertical lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the slopes are m1 and m2, then: m1 = - 1/m2 or (m1)(m2) = -1
How do you find a slope of a line perpendicular?
If two nonvertical lines are perpendicular, then the product of their slope is -1.An equivalent way of stating this relationship is to say that one line is perpendicular to another line if its slope is the negative reciprocal of the slope of the other. For example, if a line has slope 3, any line having slope - 1/3 is perpendicular to it. Similarly, if a line has slope - 4/5, any line having the slope 5/4 is perpendicular to it.
Why the product of slopes of x and y axis is -1?
The only way you can say that is from the general rule that perpendicular lines have negative reciprocal slopes. You certainly can't demonstrate it from the slopes of the axes themselves, because the slope of the x-axis is zero, and the slope of the y-axis is either infinite or else undefined, whichever term bothers you less.
Do all perpendicular lines bisect each other?
Perpendicular lines intersect."lines" are infinitely long, if you want to say that anypoint on an infinitely long line bisects that line (which IS the case in several geometrical theories but not all!) then:YES, perpendicular lines bisect each other.otherwise:NO, you cannot bisect something that is infinitly long.
Do perpendicular lines ever meet at right angles?
Whether perpendicular lines meet at right angles depends on what they are perpendicular to. Perpendicular is a relational word; this is perpendicular to that.When a pair of lines are perpendicular to each other, they are properly called "mutually perpendicular". Many people (including mathematicians) say just "two perpendicular lines" when they really mean mutually perpendicular, if it is clear from the context that that is what is meant.However, there exists at least one teacher, at least one of whom is a mathematician, who will on at least one occasion attempt to catch out at least one of his students by leading that student to make an assumption the validity of which has not been rigorously proved.This often happens when a teacher is trying to show his pupils the art of rigor in mathematical proof. (The previous paragraph is to give you some idea of what a rigorous proof looks like.)Just to formally answer the question, mutually perpendicular lines on a plane always meet at right-angles - that's what perpendicular means.
How many perpendicular lines does a star have?
A geometrical star can have various numbers of vertices, and the angles formed at the vertices need not be the same. The number of perpendicular lines depends on exactly how many vertices it has and how their angles are configured.
Pendicular lines can be parallel?
No, pendicular or can say it perpendicular lines can never be parallel as the angle b/w pendiular lines is 90 and parallel is 0 or 180 and both can not be same so ......pendicular lines cant become parallel.
What does intersect each at right angles mean?
If two lines intersect each other at right angles, that means that the measure of each angle between the two lines is 90o. Another way of stating this is to say that two lines are perpendicular.
What is the common thing parallel lines have in with perpendicular lines?
Basically, nothing. Or, you might say that in both cases, they differ by a very specific angle (in one case, 0 degrees; in the other case, 90 degrees).
Are two lines with the same y intercept are perpendicular?
Knowing that they have the same y-intercept, and knowing nothing else, the only thing you can say about the two lines is that they have the same y-intercept. That fact doesn't tell you anything else about them.
Why do gentle slopes have more widely spaced lines than steep slopes?
Presumably the questions refer to contour lines. If that is the case, the answer is as follows: Contour lines are lines drawn at selected heights on a map. They are lines that join points at the same height above the meas sea level. A gentle slope is one that does not rise (or fall) as rapidly as a steep slope. That is to say, you have to travel a greater horizontal distance to gain (lose) the same amount of vertical distance or height. So, with a gentle slope, you have to travel a greater distance to get from one contour to the next and so the lines are less close together.
How many congruent angles do two intersecting lines form?
If the lines are perpendicular, which is to say, intersect at right angles, then all four angles are congruent, since they will all be 90o. If the intersection is not perpendicular, then there are two sets of congruent angles. Opposite angles will be equal. That is to say, if you imagine the angles forming at more or less the cardinal points of the compass, the north and south angles will be equal, and the east and west angles will be equal.
