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Geometry Revision
Basic rules
Triangle Rule
Straight Line Rule
Equilateral Triangle
Vertically Opposite
Exterior Angle Rule
x
Isoscoles Triangle
y
y
x
Parallel Lines
c
a b
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.