What does the word “polygon” mean? What is the smallest number of sides a polygon can have? What...
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What does the word “polygon” What does the word “polygon” mean?mean?
What is the smallest number What is the smallest number of sides a polygon can have?of sides a polygon can have?
What is the largest number of What is the largest number of sides a polygon can have?sides a polygon can have?
Polygons with 3 sides… TrianglesPolygons with 4 sides… Quadrilaterals
Polygons with 5 sides.. PentagonsBut wait we have more polygons
Polygons with 6 sides… HexagonsPolygons with 7 sides… HeptagonsPolygons with 8 sides… OctagonsBut still we have more polygons
Polygons with 9 sides… NonagonsPolygons with 10 sides… Decagons
Polygons with 12 sides… DodecagonsAnd now we have our polygons
Hip Bone’s connected to the…Classifying Polygons
F
A B
C
DE
Important TermsA VERTEX is the point of intersection of two sides
A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL.
CONSECUTIVE VERTICES are two endpoints of any side.
Sides that share a vertex are called CONSECUTIVE SIDES.
More Important Terms
EQUILATERAL - All sides are congruentEQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent
What is the sum of the measures of the interior angles of a triangle?
180°180°
What is the sum of the measures of the interior angles of any
quadrilateral?
REVIEW:REVIEW:
180°
360°
# of sides
# of triangles
Sum of measures of
interior angles
3 1 1(180) = 180
4 2 2(180) = 360
5 3 3(180) = 540
6 4 4(180) = 720
n n-2 (n-2) 180
If a convex polygon has n sides, then the sum of the measure of the
interior angles is (n – 2)(180°)
Ex. 1 Use the regular pentagon to answer the questions.
A)Find the sum of the measures of the interior angles.
B)Find the measure of ONE interior angle
540°
108°
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
2
3
4
5
m m m m m 1 2 3 4 5 360
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
3
2
m m m 1 2 3 360
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
3
2
4
m m m m 1 2 3 4 360
Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
60°
sum of the exterior anglesnumber of sides
3606
Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
51.4°
sum of the exterior anglesnumber of sides
3607
Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?
n = 20
angleexterior sides ofnumber
anglesexterior theof sum
18360
n
Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle?
185°
Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.
30°, 90°, 150°, and 90°
Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?
n = 12