2-2 Euclidean Geometry Notes
Gr11 Theorems (taken from Mind Action series)
In order to master euclidean geometry you must know your theoroms so well that you know which theorem to
apply based on the keywords in the questions.
Here follows all the theoroms you learnt up until gr11 and the keywords associated with them
When Parallel Lines are given (highlight them)
IfBisectors
AD bisects BÂC then Â1=Â2
If CD bisects AB then AE=EB
Alternating angles are equal
B
C
D
Corresponding angles are
1
2
Â
C
A
equal
X
180 - X
E
B
D
Co-interior angles
add up to 180 or supplementary
B
Triangles
If given than  = Ĉ;
then AB=BC
If given than AB=BC;
then  = Ĉ
When the CENTRE is given you can use the following:
X
A
C
O
2X
X
(Angle at Center = 2x angle at
circumference)
O
2X
or
(Angle at circumference = ½
angle at center)
ABC is Isosceles
(= angles opp = sides)
A+B+C=180°°
(Angles of = 180)
A
1
B
2
D
C
A+B=C2
B=C2 - A
(Ext angle of )
O
2X
X
If A=B=C=60°
or
AB=AC=BC
(Equilateral )
A
If 90° given then AM = MB
(Rad⊥chord)
If AM = MB given then OM⊥
⊥AB
O
A
M
B
60°
(Line from center bisects chord)
B
60°
60°
C
All lines from center to edge of circle
are equal
O
(Radii)
When the DIAMETER is given you can use:
O
A
C
B
If given that AB is tangent then C=90°
(Rad⊥Tan)
If given that C=90° then AB is tangent
(Rad⊥Tan)
Any angle, on the edge of the circle,
subtended by diameter = 90°
(Angle in semi-circle)
When a TANGENT is given
When a CYCLIC QUAD is given
(If 4 corners of a quad is on the edge of the circle IT IS a
cyclic quad, even if the question does not tell you that it is)
B
If given that AB is tangent then C=90°
(Rad⊥Tan)
ABCD is a cyclic Quad
C
A
 + Ĉ =180° and
C
B
AC=BC
B+D=180°
(Opp angle of cyclic quad)
A
(Tangents from the same point)
D
C
A
B
D
Â=Ĉ
ABCD is a cyclic Quad
(Tangents from the same point)
CA
B
 = Ĉ1
1
(Ext ang of cyclic quad)
2
AC
B
D
B
ABCD is a cyclic Quad
2
1
2
C
1
(Tan-Chord)
A1=D1
B1=C1
A2=B2
C2=D2
(Ang in same segment)
1
2
A
The angle between the tangent and
a chord is equal to the opposite
interior angle
2 1
D
When asked to prove it is a Cyclic Quad
How to prove angles are equal if chords are given
(Most of the time the quad they ask for is outside or not
touching circles, but if you can prove the following theoroms
then the shape is a cyclic quad)
A
ϰ
100
A
In any Quad if
A+C=180° or
B+D=180°
B
1
B
D
2
If AB = BC then
D1=D2
(Angles opp = chords)
Then the shape is cyclic quad
80
ϰ
(Opp angles = 180)
180-
D
C
C
A
A
In any quad if you can
seperately prove that D1 is
the same size as B then it is a
cyclic quad
B
1
B
E
(Ext angle = interior opp
angle)
D
C
G
F
C
If 2 sircles are the same
size and have
equal chords BC=EF
then Â=Ĝ
(Angles opp = chords)
A
A
1
2
B
2
1
1
D
2
2
1
If you can prove any of these
angles = then it is a cyclic quad
A1=B1
B2=C2
A2=D2
C1=D1
(Angles in same segment)
If AB = DC then
O1=O2
(Angles at center opp
= chords)
B
1
C
O
2
D
C
A
Â=Ĉ
(Angles subtended by
same chord)
C
B
OR
(Angles in same segment)
D
Example 1
Example 2
Example 3
L
Example 4
Example 5
Example 6
Example 7
Example 8