Mathematics Paper 2 Summary Notes: Grade 12

Maths Paper 2

Notes:

, 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
= -