11.+Polygons+and+Symmetry


 * Classifying Polygons **

**Polygons ** are three or more sided closed figures with all straight sides. A circle is shape, but is not a polygon because the outside of the shape is curved, not straight. Polygons can be sorted into several different categories based on the number or length of sides, the type or measure of angles, and number of parallel lines. One way to sort polygons is into two categories, regular and irregular. **Regular polygons ** have all of the sides equal and all of the angles equal. **Irregular polygons ** do not have all of the sides or all of the angles equal. In the charts below, you will see different polygons with their names and a description of what makes them those polygons . Also included are pictures of what the polygons might look like. As long as a shape matches every part of the description of a certain polygon, even if it does not look exactly like the pictures provided, it is that type of polygon.

Five ||=  ||
 * = **Name of Polygons ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Number of **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Sides & Angles ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Pictures of Polygons ** ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Triangles || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||= [[image:Triangle.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Quadrilateral || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four  ||= [[image:Quadrilateral.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Pentagon ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Hexagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Six  ||= [[image:Hexagon.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Heptagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Seven  ||= [[image:Heptagon.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Octagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Eight  ||= [[image:Octagon.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Nonagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Nine  ||= [[image:Nonagon.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%; line-height: normal; margin-bottom: 0.0001pt;">Decagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%; line-height: normal; margin-bottom: 0.0001pt;">Ten  ||= [[image:Decagon.png]] ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Dodecagon || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Twelve  ||= [[image:Dodecagon.png]] ||

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Some triangles can fit into several categories, such as an equilateral triangle is also an acute triangle, <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">and a right triangle can also be isosceles or scalene, depending on the length of the sides.

Triangle
 * = **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;"> Names of **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Triangles ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;"> Number of Sides **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;"> & ** **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;"> Angles ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Description ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Picture of ** **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Triangles ** ||
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Equilateral

||=   <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||=     <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three equal sides  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">and angles  ||=  || Triangle ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Two equal sides  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">and angles  ||=  || than 90 degrees ||=  || than 90 degrees ||=  ||
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Isosceles
 * =   <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Scalene  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Triangle   ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">No sides equal  ||= [[image:Scalene_Triangle.png width="129" height="55" align="center"]] ||
 * =   <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Right  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Triangle  ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">One 90 degree  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">angle  ||= [[image:Right_Triangle.png width="79" height="85" align="center"]] ||
 * =   <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Acute  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Triangle  ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">All angles less
 * =   <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Obtuse  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Triangle   ||=    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Three  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">One angle greater

<span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">For quadrilaterals, a square is also a rectangle, a rhombus, and parallelogram, <span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">but not all parallelograms, rectangles, or rhombi are squares. <span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Make sure the shapes match every part of the description.

**<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Quadrilaterals ** || Opposite sides equal Opposite angles congruent ||=  || All sides equal All angles 90 degrees ||=  || Opposite sides equal
 * = **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Names of **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Quadrilaterals ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Number of Sides **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;"> & Angles ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Description ** ||= **<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">Pictures of **
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Parallelograms ||  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four  || <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Two sets of parallel sides
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Square  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Two sets of parallel sides
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Rectangle  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Two sets of parallel sides

<span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">All angles 90 degrees ||=  || Opposite angles congruent ||=  || Opposite angles congruent ||=  ||
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Rhombus  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">All sides equal
 * = <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Kite  ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">The adjacent sides are equal
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Trapezoid ||= <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Four ||=  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">One set of parallel sides  ||= [[image:Trapezoid.png]] ||

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Shapes Activity] - This activity asks you to sort quadrilaterals based on the number of equal sides, and the triangles based on the type of triangle, scalene, isosceles, and equilateral.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Triangle Quiz] - For this "quiz," all you need to focus on is identifying the different types of triangles. If you want to do any of the other topics, feel free to, but make sure you can identify the different triangles first. You can change the level, amount of time, and number of problems as you want.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Shapes Quiz] - This "quiz" asks you to identify the different polygons. You need to make sure all the boxes are checked on the left side of the screen. You can change the level, amount of time, and number of problems as you want. This is great practice for identifying the different polygons.

**<span style="color: #0c6e0c; font-family: 'Times New Roman',Times,serif; font-size: 240%;">Symmetry **

**<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 180%;">Lines of Symmetry ** <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Draw a line down the middle of a shape and fold the shape along that line. The line can be vertical, horizontal, or diagonal, like in the polygons below. If both sides are mirror images of each other, then that line is called a line of symmetry.

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Not all shapes have lines of symmetry, while others have one or more. For example, the parallelogram above cannot be folded in any way so that the halves are exactly the same on both sides (mirror images). Other shapes like the regular octagon above have many lines of symmetry. **<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 180%;">Reflection Symmetry ** <span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Reflection symmetry occurs when you put a line either in the polygon or outside of the polygon, and when you fold/flip the polygon over the line, makes an exact copy of the polygon on the other side of the line. Line symmetry is a type of reflection symmetry.





<span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">A shape has rotational symmetry if, when you turn the shape less than 360 degrees, it looks exactly the same as the original shape before the rotation.
 * <span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 180%;">Rotational Symmetry **

<span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The rectangle above has rotational symmetry at 180 degrees, since it looks exactly the same as the original. If I put the 180 degree rotation top of the original, the two would be an identical match. <span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The 360 degree rotation also is an exact match, but that is because the rectangle is back to it's original starting point.

<span style="color: #808000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">This polygon does not have rotational symmetry because the only time the rotation matches the original is when it has made a complete turn and is back at the beginning.


 * <span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 180%;">Translation **

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Translation is when you pick up the shape and move it to a new place without flipping, folding, or rotating it.



<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Symmetry Test]& [|Symmetry Review] - This "test" will see how well you understand lines of symmetry, reflection symmetry, and rotational symmetry. There is a review, if you would like it explained to you also.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Lines of Symmetry] - This video and interactive lesson on lines of symmetry will help you get a better understanding of what it is, and how to figure out if a figure has at least one or more lines.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Rotation, Translation, & Reflection Activity] - This website will show you how rotation, translation, and reflection work. You can move the figures around and see what happens.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Shape Sorter] - This activity wants you to sort the polygons into a Venn diagram. You need to pick two rules to help you sort the polygons, such as types of symmetry, types of angles, number of sides, and more. After you pick your rules, you can make your groups.

**//<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 160%;">If you have any questions about polygons or the different types of symmetry, please feel free to use the discussion tab at the top of this page, and either myself, or one of your classmates, can answer them for you. //**


 * <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 18pt;">Connecticut 6th Grade Mathematics Curriculum Standards: **

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">__Geometry and Measurement__: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;"> relationships, communicate ideas and solve problems. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">1. Classify sets and subsets of polygons using the relationship of the sides (length, parallel and <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">perpendicular) and angles (types and measure). <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 120%;">3. Identify lines of symmetry and reflections, rotations and translations of geometric figures. <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|CT Mathematics Standards]