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10.3 Polygons, Perimeters, and Tessellations HW: (1-37 Odds, 47, 49) 1 Objectives 1. Name certain polygons according to the number of sides. 2. Recognize the characteristics of certain quadrilaterals. 3. Solve problems involving a polygon’s perimeter. 4. Find the sum of the measures of a polygon’s angles. 5. Understand tessellations and their angle requirements. 2 Polygons and Perimeter • Polygon: Any ___________ _________ in the plane formed by three or more line segments that intersect only at their endpoints. • Regular Polygon: Has sides which are all the same __________ and angles of all the same ___________. • Perimeter of a Polygon: The _______ of the __________ of its sides. 3 Regular Polygons Name Triangle 3 sides Quadrilateral 4 sides Pentagon 5 sides Picture Name Hexagon 6 sides Picture Heptagon 7 sides Octagon 8 sides 4 Types of Quadrilaterals Name Characteristics Parallelogram Quadrilateral in which both pairs of opposite _________ are parallel and have the same measure. Opposite ____________ have the same measure Rhombus Parallelogram with all sides having equal ____________. Rectangle Parallelogram with four ________ angles. Because a rectangle is a parallelogram, opposite sides are __________________ and have the same measure. Square A rectangle with all sides having equal __________. Each angle measures _____, and the square is a regular quadrilateral. Trapezoid A quadrilateral with exactly ______ pair of parallel sides. Representation 5 Example 1: An Application of Perimeter Fencing costs $5.25 per foot. Find the cost to enclose the field with fencing. a. Find the perimeter. 6 Example 1 continued Fencing costs $5.25 per foot. Find the cost to enclose the field with fencing. b. Convert to feet. c. Multiply by the cost per foot. 7 Example 2: The Sum of the Measures of a Polygon’s Angles The sum of the measures of the angles of a polygon with n sides is (n – 2)180º. Find the sum of the measures of the angles of an octagon. 8 Tessellations (Tiling) • A pattern consisting of the ________________ use of the same geometric figures to completely cover a plane, leaving no _________ and no overlaps. • The sum of the measures of the angles that come together at each __________ is always _______º. 9 Examples of Tessellations 10 Example 3: Angle Requirements of Tessellations Explain why a tessellation cannot be created using only regular pentagons. Solution: Apply (n − 2)180º to find the measure of each angle of a regular pentagon. 11