simplify the expression 6y-(2y-1)-4(3y+2) a. -8y-7b. -8y-3 c. -8y+1d. -8y+7 2 1.8 warm-up 2
TRANSCRIPT
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