Polygons

Triangles and Quadrilaterals

What is a polygon?

Closed figure

At least 3 sides

Line segments are sides

Sides meet is call a vertex

More Polygon Terms

Diagonal – connects two non consecutive verticesConcave – at least one diagonal outside polygon, dented inConvex – no diagonals outside polygonPerimeter – distance around polygonArea – space polygon covers up

Define these types of Polygons pg 56

Equilateral

Equiangular

Regular

All the sides of the polygon are congruent

All the interior angles of the polygon are congruent

All sides are congruent and all angles are congruent

Types and prop of polygons

name sides

sum of interior angles

measure of each interior angle if regular polygon

sum of exterior angles

measure of each exterior angle if a regular poygon

number of diagonals

Triangles

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Undecagon

Dodecagon

N-agon

name sidessum of interior angles

measure of each interior angle if regular polygon

sum of exterior angles

measure of each exterior angle if a regular poygon

number of diagonals

Triangles 3 180 60 360 120 0

Quadrilateral 4 360 90 360 90 2

Pentagon 5 540 108 360 72 5

Hexagon 6 720 120 360 60 9

Heptagon 7 900 128.5714286 360 51.42857143 14

Octagon 8 1080 135 360 45 20

Nonagon 9 1260 140 360 40 27

Decagon 10 1440 144 360 36 35

Undecagon 11 1620 147.2727273 360 32.72727273 44

Dodecagon 12 1800 150 360 30 54

N-agon N 180(n-3) sum/n 360 360/n n(n-3)/2

Triangles – define the following pg 60

Right

Acute

Obtuse

Notice the names of all these triangles deal with the type(s) of angle the triangle has

Has only one right angle

All 3 angles are acute angles

Has only one obtuse angle

In some case why can it have only one of that type of angle?

Triangles interior angles add up to 180 and has 3 angles, if it had 2 right angles it is already at 180 and if it had 2 obtuse angles it would be over 180

More triangles pg 61

Scalene

Isosceles

Equilateral

No sides congruent

2 congruent sides, also has two congruent base angles

All sides are congruent

When naming a triangle you need to use both the name for type of angle and number of congruent sides

Notice all these triangles are named based on sides congruent

Classify vs Naming

Classify is what we use the angles and sides forNaming we use the vertices of the triangleNaming Polygons you need to go in order of vertices – either clockwise or counter clockwise, you can not skip over a vertexConsecutive vertices means one right after the other

Congruent Polygons

Polygons can be congruent but corresponding parts need to be congruentCorresponding – same location in the two polygonsCongruent angles and sidesCongruency Statement – name the polygons congruent in the correct order of congruent vertices

Examples

Naming and Congruency Statements

Quadrilaterals define and list properties pg 64

Parallelogram

Rectangle

2 pairs of parallel sidesOpposite sides congruentOpposite angles congruentConsecutive angles supplementaryDiagonals

All properties of a parallelogram andAll angles 90 degrees

Rhombus

Square

Trapezoid

Kite

All properties of a parallelogram and all sides congruent

All properties of a parallelogram and all sides congruent and all angles 90 degrees

1 pair of parallel sides, there are 3 types we will discuss later

2 pairs of congruent consecutive sides, 1 pair of congruent angles

Quadrilaterals

We will go into more depth with these shapes and come up with some additional properties as well

Homework

Due by end of classWkst AliensWkst AirlinesIn your notesPg 57 15,16,17Pg 63 15 and 16Pg 66 9 and 10