## Parallel Definition

**Parallel** sides, lines, heat segments, and rays room two lines that are always the very same distance apart and never meet. For a given line, only one heat passing with a allude not on the line will be parallel to it, favor this:

Even when we take these 2 lines the end as far to the left and also right together we can (to infinity!), lock will constantly be the very same distance apart. That method they room parallel.

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## Table the Contents

## Parallel Sides

Polygons through parallel sides could have ** one pair the parallel sides**, choose this isosceles trapezoid:

Or the polygon can have ** two pairs of parallel sides**, 2 pairs of the contrary sides the are constantly the same distance apart, choose this square and rectangle:

Or this continual octagon mirrors that you might have ** four bag of parallel sides**:

Every continuous polygon through an even number of sides will have actually pairs the parallel sides. The continuous polygon will have fifty percent as plenty of pairs that parallel sides together it has actually sides (because two sides make a pair).

That is an exciting property of regular polygons, and also of parallel sides. A continuous dodecagon (12 sides) will have actually ** six pairs of parallel sides**, but a continual tridecagon (13 sides) will have actually

*no*parallel sides.

Parallel sides of a quadrilateral, or any polygon, should be straight sides. They have the right to be sides of same length, however they execute not have to be.

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

## Parallel currently Symbol

You have the right to indicate parallel sides, even if your illustration is no perfect. Friend can additionally write around parallel present or sides using a symbol.

When drawing figures, you show pairs the parallel political parties by drawing little matching arrowheads on the 2 parallel the contrary sides.

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

In writing about parallel sides, girlfriend can additionally use this symbol: ∥

Many geometricians prefer this symbol because it can not be confused for an 11 or 2 letter Ls. Right here we are using the parallel symbol to display that line BA is parallel to heat ER:

BA∥ER

You have the right to see the if we used to letter l"s it would certainly look favor "baller," i beg your pardon is no assist at all uneven you got game.

## Proving Lines are Parallel

In a polygon, you can test because that parallel political parties by checking the notation (the little arrowheads), through measuring between the two questioned lines, or by using proofs that parallel lines native Euclid.

If you choose to measure up the distance between two sides, make certain measure follow me a line perpendicular to the 2 sides, no at one angle. Measuring the angled ends of a trapezoid, because that example, will not carry out definite proof that the 2 bases (top and bottom) are parallel, due to the fact that the two ends could be at various angles.

How can we prove lines room parallel? Euclid"s rigor is additionally helpful because you can prove parallel present using any kind of of this methods:

Congruent corresponding anglesCongruent alternative interior anglesCongruent alternative exterior anglesSupplementary inner angles ~ above the exact same side of a transversalSupplementary exterior angles on the very same side of a transversal## Parallel Shapes

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

The parallel is a special type of quadrilateral. It is named for its home of having two pairs of parallel political parties (left and right, top and also bottom) however no other limitation.

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Another interesting shape is the trapezium. That is an irregular 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 need to be maybe to:

Recognize parallel linesTest present to see if they are parallelIndicate parallel present in numbers using the ideal mathematical symbolDraw polygons having actually parallel sides