Math 6 H Periods 1, 6 & 7 (Tuesday)

Geometry PreView: Continued

Polygons: 4-5

Polygon - closed figure with at least 3 sides- no curves - no overlapping lines
Named by the number of sides (called laterals) or their number of angles
Polygon literally means MANY (poly) ANGLES (gon)

Quadrilaterals - literally means 4 laterals (sides) and angles - 360 degrees (2 triangles!)
Trapezoids - Only 1 set of parallel lines
Kite - no parallel lines - 2 adjacent sides are congruent
Parallelogram - Opposite sides parallel and congruent
Types of parallelograms:
Rhombus - all sides congruent
Rectangle - 4 right angles
Square - Rectangle with all sides congruent (so it's also a rhombus)


Regular polygons - all sides and angles congruent
2 famous ones - equilateral triangle and squares

To name a polygon-- we name its consecutive vertices IN ORDER.

A diagonal of a polygon is a segment joining two NONCONSECUTIVE vertices.

The PERIMETER of a figure is the distance around it. Thus, the perimeter of a polygon is the sum of the lengths of its sides. So to find the PERIMETER of a regular figure, you just need to know one side and multiply by the total number of sides.

Circles: 4-6
A circle is the set of all points in a plane at a given distance from a given point O called the center
A segement joining the center to a point on the circle is called a radius (plural: radii) of the circle. All radii of a given circle have the same length
A segment joining two points on a circle is called a chord, and a chord passing through the center is a diameter of the circle. The ends of a diameter divide the circle into two semicircles. The length of a diameter is called the diameter of the circle.
The perimeter of a circle is called the circumference. “Sir Cumference” – it is the ‘fence’ around it!!

The quotient Circumference ÷ diameter can be showed to be the same for all circles-- Regardless of their size. This quotient is denoted by a Greek letter π
No decimal gives π exactly!! It is non-terminating (it never ends) and non repeating!! I like to use 3.14159. In our book 3.14 is concerned a fairly good approximation.
C ÷ d = π

Formulas you need to know:
Let C = circumference d = diameter, and r = radius

Then
C = πd d = C ÷ π

C = 2πr r = C ÷ (2π)


A polygon is inscribed in a circle if all of its vertices are on the circle.
It can be shown that three points not on a line determine a circle.
There is one and only one circle that passes through the three given points.