Given: Diagram: StatementsReasons Prove: m  9 = m  2 m  6 = m  9a // b 12 43 56 87 b a t 9 Warm Up:

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Presentation transcript:

Given: Diagram: StatementsReasons Prove: m  9 = m  2 m  6 = m  9a // b b a t 9 Warm Up:

Examples Not Polygons

Convex Polygon – any polygon such that no line segment can be drawn between two vertices on the exterior of the polygon. Convex Not Convex

Regular Polygon – a polygon that is both equilateral and equiangular.

Diagonal – a segment joining two nonconsecutive vertices of a convex polygon.

Angle Measures in Polygons You can find the sum of the interior angles of a polygon by dividing a convex polygon into triangles – do this by drawing all diagonals from ONE vertex. 5 sided figure can be broken into 3 triangles. Therefore the sum of the angles would be 3 x 180  = 540 

Angle Measures in Polygons If you try this several times, you can use INDUCTIVE REASONING to hypothesize that… 6 sided figure can be broken into 4 triangles. 4 x 180  = 720  4 sided figure can be broken into 2 triangles. 2 x 180  = 360 

The sum of the measures of the angles of a convex polygon with n sides is (n – 2) x 180. A hexagon has 6 sides. What would the sum of the measures of the angles of a hexagon be? (6 – 2) x ° What would the measure of each angle be if the hexagon was regular? 720  6= 120

Exterior angle activity

The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 120° 60° 6(60) = °

Number of Sides NameSum of Interior Angles Measure of each angle (if the polygon is regular) Sum of Exterior Angles N Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-gon 180 ° 360 ° 540 ° 720 ° 900 ° 1080 ° 1260 ° 1440 ° (n - 2)x180 ° 60 ° 90 ° 108 ° 120 ° ° 135 ° 140 ° 144 ° 360 °

Ticket to leave 1.) Given a 12 sided polygon, find the sum of the measure of the interior and exterior angles. 2.) Draw a convex polygon and draw a nonconvex polygon.

Unit 3 Test of Monday. Please come prepared for class on Friday with questions. Due Friday: Packet pg 14 p Chapter Review #1-19 (skip 16a) Draw Diagrams!