Geometry Revision Basic rules Triangle Rule Straight Line

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

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)

Congruent Triangles L L x x SSS ASA SAS RHS

Parallelograms x y y x What do we know about them? • Opposite sides are equal • Opposite angles are equal • Alternate Angles

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

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

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

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

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

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

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

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

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

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

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