One type of line is called parallel means similar. ![]() Some lines are short, some lines are long, some are thin, and some are thick. We can make straight lines, we can make curved lines, and we can make wavy lines too. Lines can be used in many different ways. They are endlessly straight they go on and on and on. It is a set of points that extends infinitely in two directions. In mathematical terms, line is defined as a straight path that is endless. Lines are endless and they tend to be straight. It is not just that line-making is as ubiquitous as the use of hands and feet for gesturing and walking around respectively, but rather it’s a phenomenon which brings all the aspects of our everyday activities together into a single field of inquiry. But often are we so busy, so wrapped up in ourselves that we fail to recognize that they are there. It is fascinating because everywhere you look, there are lines. As we walk, talk, and gesticulate, we generate lines wherever we go. īoth these constructions can be proven perpendicular using the Linear Pair Perpendicular Theorem (congruent linear pairs must be 90°) or Euclid's Proposition 10, Bisecting a Straight Line.It only takes a moment to realize that lines are everywhere. Now you have ONE END to your task you created Line ED perpendicular to Line OE, through Point E. Call that Point D, and the point where your new line crosses OE can be Point N. Use a straightedge to connect Point E to the intersection of the two arcs below the line. Swing an arc below Line OE, so it crosses the other arc. Lift the drawing compass and, again without changing the distance on the compass, relocate the needle end to the other tiny arc where it crossed Line OE. ![]() Without changing the drawing compass, relocate the needle end on the left-hand arc where it intersects Line OE and swing an arc below Line OE. Strike small arcs, so you mark the two places on Line OE. ![]() Place your drawing compass needle on Point E and open the compass enough that it reaches Line OE on both the left and right ends. Given: Line OE with Point E above the line Sometimes a point is above or below a given line, and you need a perpendicular line to pass through it. Construct a perpendicular line through a point off the line Label the perpendicular line SY, so now you have some SPY coming across some APE. You could construct this with only arcs above OR below the line, but having both is a way to verify you have a perpendicular line through Point P. Swing the compass from that spot, above and below the line, so the two new arcs intersect the two most recent arcs.Ĭonnecting the two arc intersections creates a line passing through Point P. Make sure not to change the setting on the drawing compass. Without changing the distance on the drawing compass, relocate the needle end to the right-hand spot on Line AE where you first struck a tiny arc. Swing the compass above and below the Line AE, making sure you draw arcs that pass above and below Point P. ![]() Open the drawing compass up a lot more, and relocate the needle end of the drawing compass to one of the spots where the arcs cross Line AE. These are just landing spots for the next step. Swing the same distance on Line AE on either side of Point P. Open the compass, so it reaches most of the way to the end of your drawn Line AE, for great accuracy. Set the needle end of your drawing compass on Point P. This is what you are given for the beginning of the construction:Ĭonstruct: Line SY perpendicular to AE at Point PĬonstruct a perpendicular line through a point on the line Label a point, perhaps P, roughly midway across your line segment. Be sure to label two points, such as A and E, near your arrowhead ends. Begin by using a straightedge to draw a line. Perpendicular lines are easily constructed with high accuracy, whether you are an artist, mathematics student or architect.
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