Theorem 1 Vertically opposite angles are equal in measure Publish Patricia Andrews, Modified 1 years ago

Theorem 1Vertically opposite angles are equal in measure

<ABC = <EBD

&

<CBD = <EBA

Theorem 2In an isosceles triangle, the sides opposite the

equal angles are also equal in measure.

If <DFE = <DEF,

then |DE|= |FD|

Theorem 3If 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 5Two lines are parallel, if and only if, for any transversalits 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 10The diagonals of a parallelogram bisect each other.

i.e│DE│= │EB│ AND │CE│= │EA│

Theorem 15If the square on one side of a triangle is the sum of

the squares on the other two, then the angle opposite first side is 90o

i.e. If │AC│2= │AB│2+│BC│2

then <CBA =90o

Theorem 16For a triangle, base times height does not depend on

choice of baseArea of Triangle = ½ base x height

Therefore: ½ |AC| x |FB|= ½ |AB| x |DC|

Theorem 17The 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 18The 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 20Each tangent is perpendicular to the radius

that goes to the point of contact

|AP| ┴ |PC|……… where P is the point of contact

Theorem 21The 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 6If 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