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High School Geometry: Help and Review13 chapters | 162 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you will learn the special properties of parallel sides. Only certain shapes have the distinguished honor of having parallel sides. Learn what these are and also learn how to mathematically mark two sides that are parallel.

Two sides or lines are **parallel** if they are lines that are always the same distance from each other and will never intersect or touch.

The two lines above are parallel. Can you see how they are always the same distance from each other no matter where you go on either line? If you and a buddy each walked on a line, the two of you would never cross paths, and if you kept pace with each other, you would always be the same distance apart. That is what it means to be parallel.

When a shape has a pair of parallel sides, it gives the shape certain unique properties.

Look at this trapezoid. Usually when a shape has a pair of parallel sides, they make up the bases of the shape. This trapezoid has two bases with each base being one of the two parallel sides.

Also, when a shape has a pair of parallel sides, the shape's height will be the same regardless of how long you stretch it out. Take this trapezoid, for instance. If I were to stretch the shape out, it would still have the same height.

There are two ways to mathematically notate that two sides are parallel to each other. One way is by writing it with a math symbol. Another way is to note it directly on the shape using matching arrow marks on the parallel sides.

If a shape had more than one pair of parallel sides, then you would mark the difference by adding one more arrow mark to the second pair of parallel sides.

Note how this rectangle has two pairs of parallel sides and how I've marked each pair differently. The second pair has two matching arrow marks instead of just one. This lets me know that while each pair is parallel, the two pairs are not parallel to each other.

There are several shapes that have parallel sides as a distinguishing feature. The most common are the parallelogram, the rectangle, the square, and the trapezoid. These are the ones that you will most often hear about as having parallel sides.

The trapezoid has one pair of parallel sides. The parallelogram, rectangle, and square all have two pairs of parallel sides.

Other less common shapes with parallel sides include any of the '-gons' with an even number of sides, such as a hexagon, octagon, decagon, etc.

As long as these '-gons' have sides that are the same length, they will have at least one pair of parallel sides. Looking at the hexagon and octagon shown here, do you see how they have several pairs of parallel sides?

**Parallel sides** are a unique property of certain shapes. These are sides that will never meet and are always the same distance apart. Some shapes that have parallel sides include the parallelogram, the rectangle, the square, the trapezoid, the hexagon, and the octagon.

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14 in chapter 6 of the course:

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High School Geometry: Help and Review13 chapters | 162 lessons

- Angles Formed by a Transversal 7:40
- Parallel Lines: How to Prove Lines Are Parallel 6:55
- Using Converse Statements to Prove Lines Are Parallel 6:46
- Constructing a Parallel Line Using a Point Not on the Given Line 5:15
- The Parallel Postulate: Definition & Examples 4:25
- What Are Polygons? - Definition and Examples 4:25
- Regular Polygons: Definition & Parts 6:01
- How to Find the Number of Diagonals in a Polygon 4:49
- Finding the Perimeter of Polygons 5:19
- Measuring the Area of Regular Polygons: Formula & Examples 4:15
- Measuring the Angles of Triangles: 180 Degrees 5:14
- How to Measure the Angles of a Polygon & Find the Sum 6:00
- Decagon: Definition & Shape 4:55
- Parallel Sides: Definition & Concept 2:55
- Go to Parallel Lines and Polygons: Help and Review

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