ch4.7 polygons and angles
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Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Chapter 4.7Polygons and Angle Measure
Polygons are named for the number of sides they have.
3 sides = triangle 8 sides = octagon4 sides = quadrilateral 9 sides = nonagon5 sides = pentagon 10 sides = decagon6 sides = hexagon n sides = n-gon7 sides = heptagon
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Vocab
VERTEX
DIAGONAL
Vertex intersection of two sides
Diagonal segment between two nonconsecutive vertices
Key VocabREGULARA polygon is regular if it is equilateralAND equiangular
Name the following shapes by the number of sides.Are these shapes regular?
Example:What is the perimeter of a regularnonagon with a side length of 5 cm?
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
CONVEX vs. CONCAVE
Convex the diagonals are INSIDE the polygon
Concave part of the diagonals are OUTSIDE of the polygon
By drawing in all of the diagonalsfrom a vertex in a convex polygon,we can cut the shape into triangles
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
How many diagonals can be drawnfrom a vertex in a convex polygon?
# of sides # of Diagonals # of Triangles
How many DIAGONALS can be drawn in an nsided polygon?
How many TRIANGLES are in an nsided polygon?
If a polygon has n sides, we candraw n2 triangles inside of it.
5 sides3 triangles
If each of these triangles has 180 degrees.
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
(n 2) 180
IMPORTANTEIf a convex polygon has n sides,then the sum of interior angles is:
Example:Find the sum of interior angles forthe following convex polygons
Hexagon
PentagonOctagon
Heptagon
Decagon
(n 2) 180
ExampleWhat is the measure of ONEinterior angle of a regular pentagon?
Sum of interior angles(5 2) 1803 1805400
The measure of ONE angle is:540 ÷ 5 = 1080
Example:What is the measure of ONEinterior angle of a regular hexagon?
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
The sum of exterior angles for ANYconvex polygon is ALWAYS 3600
x
wz
y
t
t + x + y + z + w = 360
Example:Find the sum of exterior angles forthe following convex polygons
Hexagon
PentagonOctagon
Heptagon
Decagon
Example:What is the measure of ONEexterior angle of a regular heptagon?
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Solve for x
x
2x1050
750
350
Solve for n
1130 370
n0
n0
Ch4.7_PolygonsAndAngles.notebook October 31, 2011
Formula RecapSum of Interior <'s(n2) x 180 (n2) x 180
n
Measure of ONE Interior <
Sum of Exterior <'s Measure of ONE Exterior <
3600 3600n
Page 180:#615, 1921