## Parallel Definition

**Parallel** sides, lines, line segments, and also rays space two lines that are constantly the same distance apart and never meet. Because that a provided line, only one heat passing with a point not on that line will be parallel to it, prefer this:

Even once we take these 2 lines out as far to the left and also right together we can (to infinity!), they will always be the exact same distance apart. That way they space parallel.

You are watching: Does a triangle have parallel sides

## Table of Contents

## Parallel Sides

Polygons with parallel sides might have ** one pair that parallel sides**, choose this isosceles trapezoid:

Or the polygon could have ** two bag of parallel sides**, 2 pairs of opposite sides the are always the very same distance apart, prefer this square and also rectangle:

Or this regular octagon reflects that you can have ** four pairs of parallel sides**:

Every continual polygon through an even number of sides will have actually pairs the parallel sides. The regular polygon will have half as plenty of pairs that parallel sides as it has actually sides (because 2 sides do a pair).

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

*no*parallel sides.

Parallel sides of a quadrilateral, or any type of polygon, have to be right sides. They can be sides of equal length, however they execute not have to be.

Another residential property of parallel political parties in polygons is that the distance in between the two parallel political parties will never change, even if we elongate the shape:

## Parallel lines Symbol

You have the right to indicate parallel sides, also if your illustration is not perfect. Girlfriend can additionally write around parallel present or sides making use of a symbol.

When drawing figures, you indicate pairs the parallel sides by drawing tiny matching arrow head on the two parallel the contrary sides.

If you have, say, a rectangle (with 2 pairs the parallel sides) you have the right to use solitary arrowheads because that one pair and double arrowheads for the other:

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

Many geometricians favor this symbol since it can not be perplexed for an 11 or two letter Ls. Right here we room using the parallel symbol to present that line BA is parallel to heat ER:

BA∥ER

You deserve to see that if we supplied to letter l"s it would look like "baller," which is no assist at all uneven you acquired game.

## Proving Lines are Parallel

In a polygon, you deserve to test for parallel sides by checking the notation (the small arrowheads), by measuring between the two doubted lines, or by using proofs the parallel lines native Euclid.

If you pick to measure up the distance in between two sides, make certain measure along a heat perpendicular to the 2 sides, not at one angle. Measure the angled ends of a trapezoid, for example, will certainly not provide definite proof the the 2 bases (top and bottom) space parallel, due to the fact that the 2 ends could be at different angles.

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

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

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

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

See more: Wh A Single Water Molecule Is Held Together By : A, What Two Bonds Keep A Water Molecule Together

Another interesting shape is the trapezium. It is an rarely often, rarely quadrilateral with no parallel sides.

### Next Lesson:

What is a line Graph?

## What you learned:

After functioning your way through this lesson and video, you should be maybe to:

Recognize parallel linesTest lines to watch if they room parallelIndicate parallel lines in numbers using the ideal mathematical symbolDraw polygons having parallel sides