Parallel lines we can see around the environment
Answers
Answer:
In real life, while railroad tracks, the edges of sidewalks, and the markings on streets are all parallel, the tracks, sidewalks and streets go up and down hills and around curves. Those three real-life examples are good, but not perfect, models of parallel lines.
Answer:
The English word "parallel" is a gift to geometricians, because it has two parallel lines in it, in the form of the two side-by-side ls. It reminds you of what it means! Parallel lines are two or more lines that are the same distance apart, never merging and never diverging.
We recall that lines are never-ending, so parallel lines continue forever in two directions, always the same distance apart. A single existing line can have an infinite number of parallel lines, too, simply by picking a point not on any existing line and constructing a line parallel to all the existing ones.
To be two parallel lines, both lines must exist in the same plane. This differentiates them from skew lines, which exist in three dimensions (two separate planes).
Parallel Lines Examples
Parallel lines are by themselves very interesting, but when you take segments of them, you can construct many polygons. Think of squares, parallelograms, rectangles, and trapezoids; they all have parallel sides.
Parallel lines rule the construction industry. Buildings are erected with walls parallel to each other, ceilings are parallel to floors, and one building is usually put up parallel to other buildings on the same block.
Notebook paper is a thick collection of parallel lines. When your notebook is closed, the lines are not only parallel on each page, they are parallel from page to page, too.
Symbol for Parallel Lines
To symbolize parallel lines in geometry, we use two upright (or slightly slanted) lines, like this:
A
T
∥
U
P
AT ∥ UP
A
T
//
U
P
AT // UP
Both of those statements tell us that line
A
T
AT is parallel to line
U
P
UP.
How to Construct Parallel Lines
Construct parallel lines with a straightedge, a pencil, and plain paper. If using a ruler, this is a one-step process. Lay the ruler on the paper, holding it carefully so it does not slip. Trace each edge of the ruler. You're done!
When you move the ruler, you have parallel lines. You can label them, identifying each line with two named points and placing arrowheads at the end of the two lines.
You can also construct a line parallel to an existing line passing through a single point not on the line. You need a drawing compass plus the plain paper, pencil, and straightedge.
For the given line, draw a transversal crossing the existing line and passing through the point not on the line; we'll call that Point
A
A (for Above!). Identify the point where your new transversal intersects the existing line; call it Point
N
N (for New!)
Set your drawing compass to scribe an arc shorter than the distance from the existing line to Point
A
A.
Scribe two arcs with the compass needle set on Point
N
N and again on Point
A
A. The first arc, from Point
N
N, should cross the existing line and the transversal; the second arc, from Point
A
A, will cross only the transversal somewhere above Point
A
A.
Where your first arc crosses the transversal below Point
A
A, place your compass needle on the transversal and adjust the compass to reach the point on the existing line where your first arc crossed it.
Lift the compass, and without adjusting it, place the needle on that point above Point
A
A where the second arc intersected the transversal.
Scribe another arc down to cross that second arc.
Where the two arcs cross near Point
A
A, connect that point to Point
A
A to construct a line parallel to your existing line.
Step-by-step explanation:
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