Download Theorems 1-21 Powerpoint

Theorem 1
Vertically opposite angles are equal in measure
<ABC = <EBD
&
<CBD = <EBA
Theorem 2
In an isosceles triangle, the sides opposite the
equal angles are also equal in measure.
If <DFE = <DEF,
then |DE|= |FD|
Theorem 3
If a transversal makes alternate equal angles on two
lines, then the lines are parallel. Converse also true.
If <MPO = < LOP, then KL || MG
&
IF KL || MG then <MPO = < LOP
Theorem 5
Two lines are parallel, if and only if, for any transversal
its corresponding angles are equal. Converse also true
If KL || MG, then < LOH = <GPH
&
If < LOH = <GPH, then KL || MG
Theorem 7
<ABC is biggest angle, therefore |AC|
is biggest side (opposite each other)
Theorem 8
The length of any two sides added is always bigger than
the third side e.g │BC│+ │AB│> │AC│
Theorem 10
The diagonals of a parallelogram bisect each other.
i.e│DE│= │EB│ AND │CE│= │EA│
Theorem 15
If the square on one side of a triangle is the sum of
the squares on the other two, then the angle opposite
o
first side is 90
i.e. If │AC│2= │AB│2+│BC│2
then <CBA =90o
Theorem 16
For a triangle, base times height does not depend on
choice of base
Area of Triangle = ½ base x height
Therefore: ½ |AC| x |FB|= ½ |AB| x |DC|
Theorem 17
The diagonal of a parallelogram bisects its area
i.e. Area of Triangle ABC = ½ │AB│ x h
Area of Triangle ADC= ½ │CD│ x h
Since |AB|=|CD|; Area of both triangles are the same
Theorem 18
The area of a parallelogram is base by height
i.e. Area of Triangle ABC = ½ │AB│ x h and Area of Triangle ADC= ½ │CD│ x h.
Since |AB|=|CD|
Area of Parallelogram = 2 (½ │AB│ x h) = │AB│ x h (i.e Base x Height)
Theorem 20
Each tangent is perpendicular to the radius
that goes to the point of contact
|AP| ┴ |PC|……… where P is the point of contact
Theorem 21
The perpendicular from the centre to a chord
bisects the chord. The perpendicular bisector
of a chord passes though the centre.
If |AE| ┴ |CD|
Then.. |CE| = |ED|
Corollary 6
If two circles share a common tangent line at one point, then
two centres and that point are co-linear
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Co-linear – along the same line