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Regular Polygons

Regular Polygons. A polygon is regular if all sides and interior angles are congruent. Congruent : same size, same shape. Apothem : The altitude of each isosceles triangle from the principal angle 0. Diagonals : line segments joining two non-consecutive vertices from a given vertex.

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Regular Polygons

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  1. Regular Polygons • A polygon is regular if all sides and interior angles are congruent. • Congruent: same size, same shape

  2. Apothem: The altitude of each isosceles triangle from the principal angle 0. Diagonals: line segments joining two non-consecutive vertices from a given vertex.

  3. Constructing a Regular Polygon • Draw an isosceles triangle with 0 as the principal vertex. Angle A0B measures 72⁰ and a side length of 4cm. • Rotate the centre 0 counter-clockwise angles of 72⁰ drawing four more isosceles triangles. • Name your regular polygon and label the polygon ABCDE with centre 0.

  4. Interior Angle of a Regular polygon The sum of the interior angles of a polygon is: S = (n - 2) x 180⁰

  5. The measure a of one of the interior angles in a regular polygon is: (n – 2) x 180⁰ a = __________ n

  6. Convex and Concave A polygon is convex if each of its interior angles measure less than 180⁰. If not, then it is called “concave”. convex concave

  7. Axes of Symmetry in a Regular Polygon The axis of symmetry of a line is called: The right bisector

  8. The axis of symmetry of an angle is called The angle bisector.

  9. Perimeter of a Regular polygon P=nxc Perimeter= number of sides x side length Ex: A regular pentagon with 2 cm side length has a perimeter of: P = 5 x 2 P = 10cm

  10. Area of a Regular Polygon The area of a regular polygon is equal to: Perimeter x apothem ÷ 2 Ex: The area of a regular pentagon with side length of 8cm and the apothem measuring 3cm is: A = 5 x 8 x 3 ÷ 2 A = 60cm²

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