Angles of Polygons.

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Presentation transcript:

Angles of Polygons

What does the word “polygon” mean? Let's Discuss What does the word “polygon” mean? What is the smallest number of sides a polygon can have? What is the largest number of sides a polygon can have?

Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon Hexagon n-gon Heptagon Hendecagon

Hip Bone’s connected to the… Classifying Polygons Polygons with 3 sides… Triangles Polygons with 4 sides… Quadrilaterals Polygons with 5 sides.. Pentagons But wait we have more polygons Polygons with 6 sides… Hexagons Polygons with 7 sides… Heptagons Polygons with 8 sides… Octagons But still we have more polygons Polygons with 9 sides… Nonagons Polygons with 10 sides… Decagons Polygons with 12 sides… Dodecagons And now we have our polygons

Important Terms A VERTEX is the point of intersection of two sides F A CONSECUTIVE VERTICES are two endpoints of any side. F A B C D E A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL. Sides that share a vertex are called CONSECUTIVE SIDES.

Polygons are named by listing its vertices consecutively. F E D

More Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR - All sides and angles are congruent

Three more important terms Interior Angles Exterior Angles SUPPLEMENTARY the SUM of an interior angle and it’s corresponding exterior angle = 180o

Polygons can be CONCAVE or CONVEX

Classify each polygon as convex or concave.

It’s what’s inside that counts  Finding and using the interior angle measures of polygons

What is the sum of the measures of the interior angles of a triangle? 180° 180° 180° What is the sum of the measures of the interior angles of any quadrilateral? 360°

Sum of measures of interior angles # of triangles Sum of measures of interior angles # of sides 1(180) = 180 3 1 2(180) = 360 4 2 3 3(180) = 540 5 6 4 4(180) = 720 n-2 (n-2) 180 n

If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

If you know the sum of the angles of a regular polygon, how can you find the measure of one of the congruent angles? Regular Polygon Interior angle sum Measure of one angle Triangle 180o Quadrilateral 360o Pentagon Hexagon Heptagon Octagon Decagon Dodecagon n-gon

If a regular convex polygon has n sides, then the measure of one of the interior angles is

HOMEWORK pg 300 1-15