Lesson 3-5 Polygons.

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Presentation transcript:

Lesson 3-5 Polygons

Definitions Polygon – a closed plane figure with segments as sides. The sides intersect only at endpoints, and no endpoints are collinear.

Definitions Diagonal – a segment that connects two nonconsecutive vertices. Regular – a regular polygon is a polygon with congruent sides and angles.

Definitions

Names Sides Name 3 Triangle 9 Nonagon 4 Quadrilateral 10 Decagon 5 Pentagon 11 Hendecagon 6 Hexagon 12 Dodecagon 7 Heptagon n – Sided n-gon 8 Octagon (Ex) 27 sides 27-gon

Assignment Memorize Definitions and Polygon Names Page 161 1-10. For problems 5-7, state the name of the polygon and if the polygon is regular or not regular.

Polygon Interior Angle-Sum Theorem The sum of the measures of the interior angles of an n-sided polygon is (n-2)●180° Polygon Exterior Angle-Sum Theorem The sum of the measures of the consecutive exterior angles of any polygon is 360°

Example What is the measure of each angle of a regular heptagon? Heptagon  7 sides , so n=7 Sum of the Interior Angles=(n-2)●180° =(7-2)●180°=900° Since there are 7 sides, there must be 7 angles. So each angle would be = 900°/7= 128.6°

Assignment Page 161 11-25. For 22-25 do only the interior angle calculations.