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Euclidian Geometry

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Lines and angles Definitions of types of triangles Theorem of Pythagoras Congruency and Similarity of triangles Properties of Quadrilaterals

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Adjacent Supplementary Angles a+b = 180° Angles round a pointa+b+c = 360° y Vertically Opposite anglesVert opp angles are = Alternate anglesAlt angles are = (…//…) p Corresponding AngesCorresp angles are = (…//…) Co-interior Anglesx+y = 180° ab a b x c x y n n p x y

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Isosceles Triangle two equal sides Base angles are = Equilateral Triangle all 3 sides = in length each angle = 60° Scalene triangle all 3 sides are different all 3 angles are different

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In any right angles triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Hypotenuse² = side 1² + side 2² hypotenuse Side 1 Side 2

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Similar Triangles: these are triangles which are in proportion to each other. The lengths are the sides my differ but the angles are all the corresponding between the triangles. The triangles appear to be enlargements and reductions of each other. (AAA) Congruent Triangles: these are triangles which are identical in very way. The lengths of the sides are the same and the angles are the same. They are exactly the same in shape and size, but may differ in orientation. Four cases for Congruency: (SSS) ; (SAA) ; (SAS) ; (RHS) III

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quadrilateraltrapezium parallelogram kite rhombus rectangle square

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Solving Riders ABCD is a square. Angle E1 = 55°. Calculate the value of F1. E1 = 55 (given) A 1 = 45 (prop of square – diagonals bisect angles) F1 = (angle sum in triangle) =80° A B C D E F

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