Rotations & Reflections of Quadrilaterals & Regular Polygons

Instructor: Samantha Dixon
In this lesson, you'll learn about the math terms rotation and reflection. You'll explore what those terms mean in regards to quadrilaterals and regular polygons and discover how to solve problems relating to them.

Rotations and Reflections

Rotations and reflections are two types of transformations that can occur with shapes and objects in math. Rotation is the spinning of an object from a particular point, known as the center of rotation. When the object is spun at a particular degrees, it looks exactly the same as the original object. The angle of rotation is the angle at which the object is spun for it to look the same as the original object. The order of the object is the number of pieces or sides that looks the same.

This symbol is an example of rotation symmetry.

The recycling symbol contains an order of three because of the three arrows. The angle of rotation is 360 degrees divided by 3 = 120 degrees. This means that if the symbol is rotated from the center (center of rotation) 120 degrees, it will looks the same as the original picture. It will take three spins to get back to the original image.

Reflection can be thought of as a mirror image. When sliced in half using the line of reflection, it appears the same on both sides.

This butterfly is an example of reflection symmetry.

This butterfly has one line of reflection symmetry because if cut down the middle, the wings look the same on both sides. With both rotation and reflection, it is important to remember that size, shape, and color matter. If the butterfly had different colors on each wing, it would not have reflection symmetry. If each arrow in the recycling symbol was a different size, it would not have rotation symmetry.

Quadrilaterals and Regular Polygons

A quadrilateral is any four sided figure. Examples of quadrilaterals include a square, rectangle, parallelogram, trapezoid, rhombus, and kite. Regular polygons are polygons that are equilateral, having equal side lengths, and equiangular, having equal angles.

Reflecting and Rotating Quadrilaterals and Regular Polygons

Regular polygons are easy to reflect and rotate because they are equilateral and equiangular. In terms of reflection symmetry, the number of lines of reflection symmetry is equal to the number of sides of that polygon because each side length is the same,. For example, a pentagon is a five sided figure, so it contains five lines of symmetry.

A pentagon has five lines of symmetry.

For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. For example, an octagon is an eight-sided figure, so the order is eight. If you divide 360 by 8, you get 45, which means the octagon has an angle of rotation of 45 degrees.

An octagon has an angle of rotation of 45 degrees.

Each quadrilateral will differ in terms of rotations and reflections.

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