1. Grade 10 Mathematics
Euclidian Geometry

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

3. 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

4. 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°

5. 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

6. 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

7. Quadrilaterals trapezium parallelogram quadrilateral trapezium kite
rhombus
square
rectangle

8. 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° E D A 2 1 1 2 1 F 1 2 B C