Polygons A polygon is a plane shape with straight sides.

Plane Shapes2 Is it a Polygon? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon Not a Polygon Not a Polygon (straight sides) (has a curve) (open, not closed)

Plane Shapes3 Types of Polygons: Simple or Complex A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Simple Polygon Complex Polygon (this one's a Pentagon) (also a Pentagon)

Plane Shapes4 Types of Polygons: Concave or Convex A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°. If there are any internal angles greater than 180° then it is concave. (Think: concave has a "cave" in it) concave convex

Plane Shapes5 Types of Polygons: Regular or Irregular If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular regular irregular

Plane Shapes6 More Examples Complex Polygon Concave Octagon Irregular Hexagon (a "star polygon", in this case, a pentagram)

Plane Shapes7 Names of Polygons

Plane Shapes8 Regular 2-D Shapes - Polygons

Plane Shapes9 Triangles

Plane Shapes10 Triangles

Plane Shapes11 Combining the Names

Plane Shapes12 Quadrilateral just means "four sides" (quad means four, lateral means side). Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2-dimensional. Quadrilateral

Plane Shapes13 Four sides (or edges) Four vertices (or corners). The interior angles add to 360 degrees. Try drawing a quadrilateral, and measure the angles. They should add to 360°. Properties

Plane Shapes14 Types of Quadrilaterals There are special types of quadrilateral: If it isn't one of those it is an irregular quadrilateral. Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

Plane Shapes15 A rectangle is a four-sided shape where every angle is a right angle (90°). Also opposite sides are parallel and of equal length. The Rectangle

Plane Shapes16 The Rhombus A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

Plane Shapes17 The Square A square has equal sides and every angle is a right angle (90°). Also opposite sides are parallel. A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

Plane Shapes18 Parallelogram Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same) NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! Example: if a parallelogram has all sides equal and angles "a" and "b" are right angles, then it is also a square.

Plane Shapes19 Trapezium (US: Trapezoid) Trapezium Isosceles Trapezium A trapezium (called a trapezoid in the US) has one pair of opposite sides parallel. It is called an Isosceles trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown. A trapezoid is not a parallelogram because only one pair of sides is parallel. Language Note: In the US a "trapezium" is a quadrilateral with NO parallel sides!

Plane Shapes20 The Kite Hey, it looks like a kite. It has two pairs of sides. Each pair is made up of adjacent sides that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

Plane Shapes21 Irregular Quadrilaterals Any quadrilateral that doesn't match one of the previous types.

Plane Shapes22 The "Family Tree" Chart

Plane Shapes23 References / Sources: