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Transcript
3 Unit Maths β Plane Geometry 5 Angle sum of triangle. π π π π π β΄ π + π + π = πππ° Exterior angle of triangle. π π π π π + π + π = 180° π + π = 180° π = 180° β π β΄ π + π + 180 β π = 180 β΄ π+π= π Angle sum of quadrilateral. π π π π π π π + π + π = 180° (1) π + π + π = 180° (2) (1) + (2) β΄ π + π + π + π + π + π = πππ° Special lines in a triangle. Angle bisector An angle bisector is a line which bisects an angle. Perpendicular bisector A perpendicular bisector is a line which bisects the side and is also perpendicular to it. Median A median is the line drawn from a vertex to the midpoint of the opposite side. Altitude An altitude is a line from a vertex perpendicular to the opposite side. Thompson Ly 1 3 Unit Maths β Plane Geometry Sum of interior angles of nsided polygon. Consider; the n-gon πΌπ πππβ π£πππ‘ππ₯ ππ ππππππ π‘π 0 ππ π βππ€π, π‘βππ π π‘ππππππππ π€πππ ππππ, πππβ βππ£πππ π π π’π ππ 180° β΄ πβπ π‘ππ‘ππ πππ‘ππππππ πππππ π π’π = 180°π π»ππ€ππ£ππ, π‘βππ πππ π’ππ‘ πππππ’πππ π‘βπ ππππππ ππ‘ 0, π€βππ π π π’π ππ 360° β΄ πΊππ ππ ππππππππ ππππππ ππ ππ π β πππ = πππ°(π β π) Sum of exterior angles of nsided polygon. Consider; the n-gon ππ’π ππ πππ‘πππππ πππ ππ₯π‘πππππ πππππ ππ‘ πππβ π£πππ‘ππ₯ = 180° β΄ πβπ π‘ππ‘ππ πππ‘πππππ πππ ππ₯π‘πππππ πππππ π π’π = 180°π π»ππ€ππ£ππ, π‘βπ π π’π ππ π‘βπ πππ‘πππππ ππππππ ππ 180°(π β 2). β΄ πΊππ ππ ππππππππ ππππππ ππ ππ π β πππ = πππ° Question: Given the size of each angle in a polygon, find the number of sides. ο· Use the exterior angle property. Congruent tests Side Side Side (SSS). Side Angle Side (SAS). Angle Angle Side (AAS). Right angle Hypotunuse Side (RHS). Properties to test for quadrilaterals. Parallelogram ο· Opposite sides equal. ο· Opposite sides parallel. ο· Opposite angles equal. ο· Pair of opposite sides are equal and parallel. ο· Diagonals bisect each other. Rhombus ο· All sides are equal. ο· Diagonals bisect at right angles. Thompson Ly 2 3 Unit Maths β Plane Geometry Rectangle ο· All angles are right angles. ο· Parallelogram with equal diagonals. Square ο· All sides equal and one angle is a right angle. ο· All angles equal and two adjacent sides equal. ο· Diagonals equal and bisect each other at right angles. Intercept properties of a transversal. Properties Similar tests. Equiangular All sides in same ratio Two pairs of sides in same ratio and included angle equal. Thompson Ly 3 3 Unit Maths β Plane Geometry Pythagorasβ Theorem. π΄ π π β πΆ π΅ π π»πππ; βπ΄π΅πΆ ππ π ππππππ π‘π βπ΅πΆπ». βπ΄π΅πΆ ππ π ππππππ π‘π βπ΄πΆπ» π π»π΅ π π΄π» = πππ = π π π π π2 = ππ»π΅ πππ π 2 = ππ΄π» β΄ π2 + π 2 = π(π»π΅ + π΄π») β΄ ππ + ππ = ππ Areas Triangle π¨= π ππ π β π Parallelogram π¨ = ππ β π Trapezium π+π π¨ = π( ) π π β π Thompson Ly 4 3 Unit Maths β Plane Geometry Rhombus π¨ = ππ or π¨= π π ππ π¦ β π₯ π Rectangle π¨ = ππ β π Square π¨ = ππ π₯ Thompson Ly 5
