Grade 10 Mathematics Euclidian Geometry

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

Lines and Angles Adjacent Supplementary Angles a+b = 180° Angles round a point a+b+c = 360° y Vertically Opposite angles Vert opp angles are = Alternate angles Alt angles are = (…//…) p Corresponding Anges Corresp angles are = (…//…) Co-interior Angles x+y = 180° b a a b c x x y n n p x y

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

Theorem of Pythagoras 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

Similar and Congruent Triangles 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 III

Quadrilaterals trapezium parallelogram quadrilateral trapezium kite rhombus square rectangle

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 = 180-55-45 (angle sum in triangle) =80° E D A 2 1 1 2 1 F 1 2 B C