1 GRADE 11 MATHEMATICS PAPER 3 GEOMETRY ... - AdMaths

5.4 EXAMPLES
Example 1
If we have to prove that BD 2 = AD.DC, we must prove ∆ ABD similar to
∆ BCD ( BD is the common side ) .
Name the similar triangles in the following figures and calculate the values of
c m
a , b , x , y , and .
d n
a) b)
c) d)
L
Solution
A
24
B
a) ∆ AEB ∆DEC ( Â = alternate Dˆ and Bˆ = alternate Ĉ )
Hence
18
E
d
15 30
K
AE
DE
18
30
=
=
a
c
N
EB
EC
15
a
=
C
D
=
b
7,5 P 17,5 S
M
m
M
n
AB
DC
24
b
Hence 18a = 15 × 30 and 18b = 30 × 24
a = 25 b = 40
16
Q
S
24
P
36
x
P
30
21
R
T
y
32
R
T
10