POLYGONS 10/17/2007 NAMING POLYGONS

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Presentation transcript:

POLYGONS 10/17/2007 NAMING POLYGONS EQ: How do I find the measure of an interior & exterior angle of a polygon?

What does the word “polygon” mean? 10/17/2007 POLYGONS 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? EQ: How do I find the measure of an interior & exterior angle of a polygon?

Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon POLYGONS 10/17/2007 Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon Hexagon n-gon Heptagon EQ: How do I find the measure of an interior & exterior angle of a polygon?

Important Terms A VERTEX is the point of intersection of two sides F A 10/17/2007 POLYGONS Important Terms A VERTEX is the point of intersection of two sides 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. EQ: How do I find the measure of an interior & exterior angle of a polygon?

More Important Terms EQUILATERAL - All sides are congruent 10/17/2007 POLYGONS More Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR - All sides and angles are congruent EQ: How do I find the measure of an interior & exterior angle of a polygon?

Diagonals & Angle Measures 10/17/2007 POLYGONS 10/17/2007 Diagonals & Angle Measures EQ: How do I find the measure of an interior & exterior angle of a polygon?

What is the sum of the measures of the interior angles of a triangle? REVIEW: POLYGONS 10/17/2007 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° EQ: How do I find the measure of an interior & exterior angle of a polygon?

POLYGONS 10/17/2007 If a convex polygon has n sides, then the sum of the measure of the interior angles is (n-2)(180°) EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 1 Use the regular pentagon to answer the questions. 10/17/2007 POLYGONS Ex. 1 Use the regular pentagon to answer the questions. Find the sum of the measures of the interior angles. Find the measure of ONE interior angle 540° 108° EQ: How do I find the measure of an interior & exterior angle of a polygon?

Two more important terms POLYGONS 10/17/2007 Two more important terms Interior Angles Exterior Angles EQ: How do I find the measure of an interior & exterior angle of a polygon?

10/17/2007 POLYGONS 1 2 3 4 5 If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. EQ: How do I find the measure of an interior & exterior angle of a polygon?

10/17/2007 POLYGONS If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2 EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 2 Find the measure of ONE exterior angle of a regular hexagon. POLYGONS 10/17/2007 Ex. 2 Find the measure of ONE exterior angle of a regular hexagon. 60° EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 3 Find the measure of ONE exterior angle of a regular heptagon. POLYGONS 10/17/2007 Ex. 3 Find the measure of ONE exterior angle of a regular heptagon. 51.4° EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 4 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle? POLYGONS 10/17/2007 185° EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 5 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle. POLYGONS 10/17/2007 30°, 90°, 150°, and 30° EQ: How do I find the measure of an interior & exterior angle of a polygon?

Ex. 6 The sum of the interior angles of a polygon is 720 Ex. 6 The sum of the interior angles of a polygon is 720. Find the number of sides. POLYGONS 10/17/2007 n = 6 EQ: How do I find the measure of an interior & exterior angle of a polygon?

POLYGONS 10/17/2007 Homework: Page 300 # 1-21 EQ: How do I find the measure of an interior & exterior angle of a polygon?