Terminology

1. Triangle- a closed* shape in a plane consisting of three line segments
2. *Closed- every endpoint of one of the line segments meets exactly one endpoint of another line segment
3. Hypotenuse- the side opposite the right angle in a right triangle

Special Kinds of Triangles

1. Right triangle- a triangle that has a right angle
2. Equilateral triangle- a triangle that has three sides of the same length
3. Isosceles triangle- a triangle that has at least two sides of the same length

Other Shapes

1. Quadrilateral- a closed shape in a plane consisting of four line segments that do not cross each other

The line segments making the polygon are called its sides, and the points where line segments meet are called the vertices (singular: vertex).

1. Polygon- a closed, connected shape in a plane consisting of a finite number of line segments that do not cross each other

Triangles are polygons with three sides.

Quadrilaterals are polygons with four sides.

Pentagons are polygons with five sides.

Hexagons are polygons with six sides.

Octagons are polygons with eight sides.

A polygon with n sides can be called an “n-gon.” For example, a polygon with fifteen sides is a 15-gon.

A circle is not a polygon. Why not? It is not a polygon because it is not made by a line segment?

Polygon = many angles

Regular polygon- all sides have the same length, and all angles are equal

• An equilateral triangle and a square are regular polygons

A pentagon, hexagon, octagon, etc. can be regular or irregular polygons.

Special Quadrilaterals

1. Square- a quadrilateral with four right angles whose sides all have the same length
2. Rectangle- A quadrilateral with four right angles
3. Rhombus- A quadrilateral whose sides all have the same length; the name diamond is sometimes used instead of rhombus
1. A square is a rhombus, but a rhombus is not a square.
4. Parallelogram- a quadrilateral for which opposite sides are parallel
5. Trapezoid- a quadrilateral for which at least one pair of opposite sides are parallel (some books define a trapezoid as a quadrilateral for which exactly one pair of opposite sides are parallel)
1. A square, rectangle, rhombus, and parallelogram are all trapezoids.

Diagonals of a quadrilateral- line segments connecting opposite corner points

Kite- a quadrilateral with two pairs of equal sides, and the equal pairs have a common vertex

Showing Relationships with Venn Diagrams

1. Venn diagram- a picture that shows how certain sets are related
2. Set- a collection of objects