Polygons Math 2A: [10-6] Polygons

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Presentation transcript:

Polygons Math 2A: [10-6] Polygons Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

Math 2A: [10-6] Polygons »A polygon is a simple, closed figure formed by three or more straight lines. »Examples: »Non-Examples: Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

»Polygons are named by the number of sides they have. Math 2A: [10-6] Polygons 3 Sides… Triangle 4 Sides… Quadrilateral 5 Sides… Pentagon Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

6 Sides… Hexagon 7 Sides… Heptagon 8 Sides… Octagon 9 Sides… Nonagon Math 2A: [10-6] Polygons 6 Sides… Hexagon 7 Sides… Heptagon 8 Sides… Octagon 9 Sides… Nonagon Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

10 Sides… Decagon n Sides… n-gon Ex: 21-gon Math 2A: [10-6] Polygons 10 Sides… Decagon n Sides… n-gon Ex: 21-gon »A polygon that has all sides and angles congruent is called a regular polygon. Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

»Classify each polygon and state whether it is regular »Classify each polygon and state whether it is regular. If it is not a polygon, explain why. Math 2A: [10-6] Polygons Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

1. A quadrilateral is a closed figure with four sides and four angles. Math 2: [10-5] Quadrilaterals 1. A quadrilateral is a closed figure with four sides and four angles. 1. The quadrilateral family tree: 6. 2. 3. 4. 5. Sunshine State Standards: MA.C.1.1.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6

2. A parallelogram is a quadrilateral with two pair of parallel sides. Math 2: [10-5] Quadrilaterals 3. A rectangle is a quadrilateral with four right angles. Sunshine State Standards: MA.C.1.1.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6

4. A rhombus is a quadrilateral with 4 congruent sides. Math 2: [10-5] Quadrilaterals 4. A rhombus is a quadrilateral with 4 congruent sides. 5. A square is a quadrilateral with 4 right angles and 4 congruent sides. Sunshine State Standards: MA.C.1.1.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6

6. A trapezoid is a quadrilateral with 1 pair of parallel sides. Math 2: [10-5] Quadrilaterals 1 2 3 4 The sum of the angles in any quadrilateral is always 360°. 1 + 2 + 3 + 4 = 360° Sunshine State Standards: MA.C.1.1.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6

Find the missing angles. Math 2: [10-5] Quadrilaterals Find the missing angles. 45° 55° 100° x° 118° 50° 80° y° Sunshine State Standards: MA.C.1.1.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6

»This formula can be used to find the angle sum of any polygon: Math 2A: [10-6] Polygons A = 180(n − 2) Angle Sum Number of Sides A = 180(n − 2) Divide by n to find each angle. A = 180(4 − 2) A = 180(2) A = 360°  4 = 90° Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

»Find the measure of each interior angle in a regular octagon. Math 2A: [10-6] Polygons Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

»Perimeter is the distance around any polygon. Math 2A: [10-6] Polygons »What is the perimeter of this regular pentagon? 2.4 m 5 × 2.4 = 12 m »A repetitive pattern of polygons that fit together with no overlaps or holes is called a tessellation. Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4

Math 2A: [10-6] Polygons BW: [10-6] Review »Find the measure of each interior angle, round to the nearest tenth if necessary. Regular dodecagon (12 sides) Regular undecagon (11 sides) 34 Sunshine State Standards: MA.B.1.3.1-1, MA.C.1.3.1-4