POLYGON PROPERTIES @ 9B

Types of Angles A reflex angle is more than 180° An acute angle is less than 90° An obtuse angle is more than 90 ° but less than 180° A right angle equals 90° 90 °

Angle Properties Angles at a point add to 360° a + b + c + d = 360° Angles on a straight line add to 180°. a + b + c = 180° Vertically opposite angles are equal . b b a a c b a d c b a

Parallel Lines e + f = 180° d d c c b b a a Alternate angles are equal. Corresponding angles are equal. f e Interior angles add to 180°.

Triangles The sum of the angles of a triangle is 180° a + b + c = 180° Equilateral triangles have 3 equal sides and 3 equal angles. Isosceles triangles have 2 equal sides and 2 equal angles. c a b a a 60° 60° 60°

Exterior angles of a triangle The exterior angle of a triangle is equal to the sum of the interior opposite angles. i.e.  ACD =  ABC +  BAC interior opposite angles exterior angle A B C D

20° C A B D E Find  CED  CDE  EAB 60° 55°  CAE  ACE  ABE  AEB Example = 40° 40° = 40° 40° = 120° 120° = 85° 85° 35° = 35° = 20° 20° = 120° 120°

Quadrilaterals p + q + r + s = 360° It can be split into 2 triangles. The sum of the angles of a quadrilateral = 2 x 180° = 360°. A quadrilateral has 4 sides. p q r s

Interior angles of polygons The sum of the interior angles of any pentagon = 3 x 180° = 540° It can be split into 3 triangles. p q r s t p + q + r + s + t = 540 ° A pentagon has 5 sides.

Regular Polygons quadrilateral 180° 1×180 o 360° pentagon 540° hexagon 720° heptagon 900° Interior angles of a polygon with n sides add to ( n – 2) × 180°. 2×180 o 3×180 o 4×180 o 5×180 o n-gon (n-2)×180 o No. of sides Name Sum Pattern 3 triangle 4 5 6 7 ... ... n

Exterior angles of a polygon Exterior angles of a polygon add to 360°. At each vertex: interior angle + exterior angle = 180° a + b + c + d + e = 360° b a c e d

Regular Polygons quadrilateral 180° 60° 360° 90° pentagon 540° 108° hexagon 720° 120° heptagon 900° 129° octagon 1080° 135° nonagon 1260° 140° decagon 1440° 144° What is the exterior angle of each regular polygon? Is the total 360° in each case? No. of sides Name Angle Sum Interior Angle 3 triangle 4 5 6 7 8 9 10

Find  ABC Example  ADC  BAC  CAD ABCDE is a regular hexagon with centre O.  ACD  ODE  EOD = 120° 120° = 60° 60° = 30° 30° = 30° 30° C A B D E F O = 90° = 60° 60° = 60° 60°

POLYGON PROPERTIES @ 9B

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POLYGON PROPERTIES @ 9B