These notes are described in full and complete detail and are easy to understand. They cover all the work in Mathematics Paper 2 for Grade 12. These notes cover the topics: Trigonometry, Euclidean Geometry, Analytical Geometry and Statistics. Formulas and steps are provided.
, Straight lines:
sum of angles on straight lines must add up
to 180. [I's on str lined
x 60
x 40 00 180
+ +
= I's on str line
x 180 = -
60 -
40
·C 80:
=
Triangles:
1) Sum of angles of triangle 180
=
2) exterior angles
Q
-
2 L
P R E
RS:sum of interior opposite angles.
p+
=
, Parallel Lines:
f
A 0
M. B
/
I
-
L vert opp
S
↑
C >
~ - D
G
t
fHB = ANG
- -
vert opp angles
AHG HGD =
Alt L's ABIICD A
-
S
corresp ('s
FHB HGD =
1
ABIICD f
AHG + (GH =180 co-intL's ABIICD L
Types of triangles:
1) Scalene triangles
-
I M
2) isoceles triangle:
B
only two sides are
- 9HA1.
Al ~ c[basel's of isos 3
=
3)equiliteral triangle:
- all sides and angles
are equal
o60.
, congurency: -
- all congurent U are similar
if itake two triangles and put them on top
of each other they will be exactly equal.
proving congurency:
B
E
11 - - - -
sides are equal
A III cD III F
AB:DEgiven
BC:of given
AC:DA given
ABC UDE
:. [SSS]
Q T
2) -
-
E
two angles, one side
P
3
A R s Yr H B E
4) -
- - -
P5 =
given
p I f
aI =
given
A CD
PR SU
=
given AC DF
=
given
:.UPARESTU [LLS] BC EF
=
given
Q A B
=
right(
E
3) two sides and an ABC UDEf =
(RHS]
- -
included angle.
D "of P
R
DE PQ
=
given
IF QR
=
given
B = given
:DEF = QPR [SSL]
, Similar Triangles:
We getsimilar triangles that aren't congurent.
B Z
not similar in terms of size,
~ -
butin proportion to each side.
7 ~
↳ ~ CD
f
A
if we have three angles that are equal,
itdoes not mean congurency but similarity.
AI =
given
B E =
given
i F =
given
: ABC III ↓DEF
Similar I congurent
theorem of Pythagoras:
x
Al F C
BC2 AB +ACL
=
I 98 39
= -
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