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Math 1 March 14 th WARM-UP: 1. TW = 24TS = 10 RU = 12 S is the centroidFind the measures of these segments: a) TU b) SV c) TV d) RS e) SU

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POP QUIZ TOMORROW!!

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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?

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

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F AB C DE Important Terms A 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.

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

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Polygons are named by listing its vertices consecutively. AB ED C F

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Polygons can be CONCAVE or CONVEX CONVEX CONCAVE

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Ex. 3 Classify each polygon as convex or concave.

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

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# of sides # of triangles Sum of measures of interior angles 31 1(180) = 180 42 2(180) = 360 5 33(180) = 540 644(180) = 720 n n-2 (n-2) 180

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

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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°

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Two more important terms Exterior Angles Interior Angles

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If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 2 3 4 5

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1 3 2

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1 3 2 4

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Ex. 2 Find the measure of ONE exterior angle of a regular hexagon. 60°

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Ex. 3 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

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Ex. 4 Each exterior angle of a polygon is 18 . How many sides does it have? n = 20

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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°

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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°

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Ex. 7 If each interior angle of a regular polygon is 150 , then how many sides does the polygon have? n = 12

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Foldable for Formulas

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