Simplify the expression Simplify the expression 6y-(2y-1)-4(3y+2)6y-(2y-1)-4(3y+2)

a. -8y-7a. -8y-7 b. -8y-3b. -8y-3

c. -8y+1c. -8y+1 d. -8y+7d. -8y+7

2

1.8 warm-up 2

Polygon Angle-Sum Polygon Angle-Sum TheoremsTheorems

Pardekooper

Lets start with some Lets start with some common terms.common terms.

• PolygonPolygon– A closed plane figure with A closed plane figure with

at least three sides that at least three sides that are segments. The sides are segments. The sides

intersect only at their intersect only at their endpoints, and no endpoints, and no adjacent sides are adjacent sides are

collinear.collinear.

Pardekooper

Yes

Pardekooper

No, it has

no sides

No, it is nota planefigure

No,two sidesIntersectBetween endpoints

Lets start with some Lets start with some common terms.common terms.

• Regular PolygonRegular Polygon– All the sides are congruentAll the sides are congruent

– All the angles are All the angles are congruentcongruent

Pardekooper

Name all the polygons Name all the polygons belowbelow

AA

Pardekooper

BBCC

DDEE

polygon ABCDEpolygon ABCDE

polygon ABEpolygon ABE

polygon BCDEpolygon BCDE

Now name the parts of Now name the parts of the polygonthe polygon

AA

Pardekooper

BBCC

DDEE

Vertices: A, B, C,D,E,

Sides: AB, BC, CD,DE,EA

Angles: A,B,C,D,E

Lets name the polygons

7 heptagon

11 hendecagon

5 pentagon

6 hexagon

Pardekooper

# of sides name

3 triangle

4 quadrilateral

8 octagon

9 nonagon

10 decagon

12 dodecagonn n-gon

How about different types How about different types of polygonsof polygons

Convex polygons

no diagonal with points outside the polygon

Pardekooper

How about different types How about different types of polygonsof polygons

Concave polygons

at least one diagonal with points outside the

polygon

Pardekooper

Just two more theorems !Just two more theorems !

Polygon Angle-Sum Theorem

Pardekooper

The sum of the measures of the interior angles of a n-gon is

(n-2)180.Example:

Find the sum of the measures of the angles of a 15-gon.

n = 15formula: (n-2)180

(15-2)180

(13)1802340

Pardekooper

11701000

x0

11501050

How many sides ?

5 sides

Use the formula tofind out how

many degrees.(n-2)180

(5-2)180(3)180

540

Just one more theorem !Just one more theorem !

Polygon Exterior Angle-Sum Theorem

Pardekooper

The sum of the measures of the exterior angles of a polygon, one at

each vertex is 360.

1

23

4

56

m1 + m2 + m3 + m4 + m5 + m6 = 360