1. Geometry Revision Basic rules
Triangle Rule Straight Line Rule Exterior Angle Rule Isoscoles Triangle
Equilateral Triangle
Vertically Opposite y x x y

2. Parallel Lines
a b
c d
e f
g h
<a = <e (corresponding) <a = <h (alternate) <a = <d (Vertically Opposite)
<b = <f (corresponding)
<b = <g (alternate)
<b = <c (Vertically Opposite)

3. Congruent Triangles L x L
RHS
SSS
ASA
SAS

4. Parallelograms What do we know about them? Opposite sides are equalx
What do we know about them?
Opposite sides are equal
Opposite angles are equal
Alternate Angles y

5. Circumcentre/circumcircle
What we know about it:
Constructed by bisecting each SIDE
Centre of circle is equal distance from each corner.

6. Incentre/Incircle What we know about it:
Constructed by bisecting each ANGLE
Centre of circle has the same perpendicular distance from each side.

7. Circle Theorems
One angle at the centre and one angle at the circumference, BOTH STANDING ON THE SAME ARC
What do we know about this diagram?
The angle at the middle is twice the size of the angle at the centre

8. Deductions of previous theorem Diameter
An angle standing on the diameter that meets at the circumference ALWAYS equals 90⁰

9. Two angles standing on the same arcx
Two angles meeting at the circumference, standing on the same arc are always equal x

10. Cyclic Quadrilateral
A cyclic quadrilateral is a quadriltaral where all four corners touch the circle
Opposite angles in a cyclic quadrilateral always add up to 180⁰

11. Tangents
A line is a tangent if it is perpendicular to a line joining the centre of a circle to a point on the circumference of that circle or
If a line is a tangent at a point, then it is perpendicular to a line joining that point to the centre

12. Chords
If a line is perpendicular to a chord and joins the centre, then that line bisects the chord.
i.e. bc = ca
Also <ocb and <oca = 90⁰
Hint: OB and OA are the radius

13. Line Perpendicular to the side of a triangle
All the sides are cut in proportion 1. 2. 3.

14. Similar Triangles
In similar triangles, all angles are equal Also all sides are in proportion, i.e. a
b c d
e f

15. Pythagoras theorem
Usually used any time a RIGHT ANGLED TRIANGLE is mentioned. x² + y² = z² Remember: z HAS to be the hypotenuse. z x y