Intersecting Lines
Non interesting lines are called lines
Non-perpendicular intersecting lines. There is no special name.
By definition, any lines/segments that are perpendicular to each other either do, or (in the case of non-intersecting segments) would, intersect each other at right angles. A right angle being a 90* angle. Therefore, perpendicular, intersecting line segments will form 4 90* angles.
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
you can check if two equations are parallel, perpendicular or neither by comparing their slopes. If the slope of one linear equation is identical to the other or is a multiple of it then they are either parallel or perpendicular. ex. Slope of line "A" is 4/3 Slope of line "B" is 8/6 because slope B is equal to 4 times slope A they are parallel. This is whats known as a scalar multiple. it just means that they both head in the exact same direction even though one is a little bit larger than the other one. Also note that if two equations do have similar or equal slopes, you must also check to see if they are identical lines (coincide) or if they are lines that are parallel but never touch each other (parallel and distinct). To do this, take any point that contains both and X and Y variable that is not 0 from one equation and input it into the other equation. See if the Y you put into the equation is what you get when you calculate the x side of the formula. Ex. (Line "A") y=m(x)+b (Line "B") y=m(x)+b if line A is Y=4/3(x)+1 then set x to any non zero value and solve for it y=4/3(3)+1=5 thus, one point on line A is (3,5) now put this point into Line"B" and see if the left hand side is equal to the right hand side (LHS=RHS) Line"B" y=m(x)+b if line B is y=8/6(x)+1 then when you input the values from Line A you get 5=8/6(3)+1 LHS=5 RHS=5 They are equal, this means that this point exists on this line. Thus both lines are on top of each other or more noticeably. Both equations represent the same line. To calculate if the lines are perpendicular you also compare the slopes of both lines. If one line is perpendicular to the other then their slopes will be negative inverses of one another. In lament terms, they are as follows. Slope "C" = 7/4 Slope "D" = -4/7 The line of "C" is perpendicular to the line of "D" the slopes must have their fractions inverted (flipped upside down) and their sign must be also switched from either positive to negative or from negative to positive.
Non interesting lines are called lines
Non-perpendicular intersecting lines. There is no special name.
intersecting lines * * * * * Non-perpendicular intersecting lines. Or else the angles would be right angles.
intersecting lines * * * * * Non-perpendicular intersecting lines. Or else the angles would be right angles.
If the planes are non-intersecting, then they're parallel. Any line that intersects one of them intersects both of them.
By definition, any lines/segments that are perpendicular to each other either do, or (in the case of non-intersecting segments) would, intersect each other at right angles. A right angle being a 90* angle. Therefore, perpendicular, intersecting line segments will form 4 90* angles.
Non-perpendicular intersecting lines.
Lines that meet at any angle other than 90 degrees.
If the intersected lines are parallel then the angles are called equal alternate angles
Upper-case (capital) A, K, M, N, V, W, X, Y, Z
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
Here are some: They can be (1) coincident, (2) intersecting at one point, (3) coplanar but non-intersecting (ie parallel), (4) non-coplanar, non-parallel and non-intersecting (eg paths of a rail line and of an elevated road going over it - from above, they may appear to intersect but they do not), (5) intersecting at two points (eg longitudes on the earth). etc.