## Parallel Definition

**Parallel** sides, lines, line segments, and rays room two lines that are constantly the exact same distance apart and never meet. For a offered line, just one heat passing through a allude not on the line will certainly be parallel to it, favor this:

Even as soon as we take these 2 lines out as much to the left and also right together we have the right to (to infinity!), castle will always be the same distance apart. That method they room parallel.

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## Table that Contents

## Parallel Sides

Polygons with parallel sides might have ** one pair of parallel sides**, prefer this isosceles trapezoid:

Or the polygon can have ** two bag of parallel sides**, two pairs of the opposite sides the are always the same distance apart, choose this square and also rectangle:

Or this constant octagon shows that you might have ** four bag of parallel sides**:

Every constant polygon with an even number of sides will have pairs of parallel sides. The continual polygon will certainly have half as countless pairs the parallel sides together it has actually sides (because two sides do a pair).

That is an interesting property of consistent polygons, and of parallel sides. A constant dodecagon (12 sides) will have ** six pairs that parallel sides**, yet a continual tridecagon (13 sides) will have actually

*no*parallel sides.

Parallel political parties of a quadrilateral, or any polygon, must be straight sides. They can be sides of same length, however they carry out not have to be.

Another residential property of parallel political parties in polygon is that the distance in between the 2 parallel political parties will never change, even if us elongate the shape:

## Parallel lines Symbol

You can indicate parallel sides, also if your drawing is no perfect. Friend can likewise write about parallel lines or sides using a symbol.

When illustration figures, you indicate pairs of parallel political parties by drawing small matching arrowheads on the two parallel opposite sides.

If friend have, say, a rectangle (with 2 pairs the parallel sides) you can use single arrowheads because that one pair and twin arrowheads for the other:

In writing around parallel sides, friend can additionally use this symbol: ∥

Many geometricians favor this symbol since it cannot be confused for an 11 or 2 letter Ls. Here we space using the parallel prize to display that line BA is parallel to line ER:

BA∥ER

You can see the if we used to letter l"s it would look prefer "baller," which is no assist at all unless you gained game.

## Proving Lines space Parallel

In a polygon, you can test for parallel sides by check the notation (the little arrowheads), by measuring between the two doubted lines, or by applying proofs of parallel lines indigenous Euclid.

If you select to measure up the distance between two sides, make certain measure along a line perpendicular to the 2 sides, not at an angle. Measure the angled end of a trapezoid, for example, will not provide definite proof the the two bases (top and also bottom) are parallel, due to the fact that the 2 ends can be at different angles.

How can we prove lines are parallel? Euclid"s rigor is additionally helpful since you have the right to prove parallel lines using any kind of of this methods:

Congruent equivalent anglesCongruent alternate interior anglesCongruent alternative exterior anglesSupplementary inner angles on the same side the a transversalSupplementary exterior angle on the exact same side that a transversal## Parallel Shapes

We know that many species of quadrilaterals, such as the trapezoids, a rhombus, rectangles, and all the constant polygons (except because that the triangle), have parallel sides. One other shape has parallel sides: the **parallelogram**.

The parallel is a special form of quadrilateral. The is called for its residential property of having actually two pairs of parallel political parties (left and also right, top and bottom) but no various other limitation.

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Another interesting shape is the trapezium. The is an rarely often, rarely quadrilateral through no parallel sides.

### Next Lesson:

What is a line Graph?

## What friend learned:

After working your method through this lesson and video, you have to be maybe to:

Recognize parallel linesTest currently to view if they room parallelIndicate parallel present in figures using the proper mathematical symbolDraw polygons having actually parallel sides