What is a polygon Sum of interior angles in polygons Polygon How can I find angle measures in polygons without using a protractor Polygon Polygon comes from Greek Poly means many gon ID: 305682
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Slide1
Learning intentions:What is a polygon?Sum of interior angles in polygons.
PolygonSlide2
How can I find angle measures in polygons without using a protractor?Slide3
PolygonPolygon comes from Greek. Poly- means "many"
gon
means "angle".
Many anglesSlide4
What is a polygon?A polygon is a Plane shape with straight sides.Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).Resource:
http://www.mathsisfun.com/geometry/polygons.htmlSlide5
PolygonsSlide6
NonexamplesSlide7
Types of PolygonsRegular or IrregularIf all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
Concave or Convex
A
convex
polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is
concave
. (
Think: concave has a "cave" in it
)
C
onvex
C
oncave
http://www.mathsisfun.com/geometry/polygons.htmlSlide8
PolygonsCan be concave or convex. Concave Convex
Non-convex polygons have some diagonals
that do
not
lie within the figure. Some interior
angles are reflex (greater than 180
°).
The diagonals of the convex
polygon
all lie within the
figure.Slide9
Polygons are named by number of sidesNumber of Sides
Polygon
3
4
5
6
7
8
9
10
12
n
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gonSlide10
Sums of Interior AnglesSlide11
Draw a: Quadrilateral Pentagon Hexagon Heptagon Octogon Then draw diagonals to create triangles.A diagonal is a segment connecting two nonadjacent vertices (don’t let segments cross)Add up the angles in all of the triangles in the figure to determine the sum of the angles in the polygon.Complete this table
Polygon
# of sides
# of triangles
Sum of interior anglesSlide12
Sums of Interior Angles
Triangle
Quadrilateral
Pentagon
Heptagon
Octagon
Hexagon
= 2 triangles
= 3 triangles
= 4 triangles
= 5 triangles
= 6 trianglesSlide13
Polygon
# of sides
# of triangles
Sum of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon
3
4
5
6
7
8
n
3
4
5
6
n - 2
2
1
180°
2
x
180 = 360°
3
x
180 = 540°
4
x
180 = 720°
5
x
180 = 900°
6
x
180 = 1080°
(n – 2)
x
180°Slide14
Polygon
# of sides
# of triangles
Sum of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon
3
4
5
6
7
8
n
3
4
5
6
n - 2
2
1
180°
2
x
180 = 360°
3
x
180 = 540°
4
x
180 = 720°
5
x
180 = 900°
6
x
180 = 1080°
(n – 2)
x
180°Slide15
The angle sum of a polygon with n sides is given by:angle sum = (n − 2) × 180° or 180(n − 2)°Find the angle sum of a polygon with 18 sides.SolutionAngle sum = (18 − 2) × 180°= 16 × 180°= 2880°Find the angle sum of a polygon with sides.SolutionAngle sum = (4
− 2) × 180°
= 2
× 180°
=
360°.Slide16
End