LESSON 1 – PROPERTIES OF SIMILAR TRIANGLES
Two identical pictures BUT one is bigger than the
other.
CONGRUENT TRIANGLES



SIMILAR TRIANGLES
Same size and shape
Corresponding angles are equal
Corresponding sides have the same
length



Same size and shape
Corresponding angles are equal
Corresponding side lengths are in proportion
𝐵
𝐴
𝐷
𝐶
𝐹
𝐶
𝐴
𝐷
∆𝐴𝐵𝐶~∆𝐷𝐸𝐹
∆𝐴𝐵𝐶 = ∆𝐷𝐸𝐹
∠𝐴 = ∠𝐷
∠𝐵 = ∠𝐷
𝐸
𝐵
𝐸
∠𝐴 = ∠𝐷
∠𝐶 = ∠𝐹
𝑎
𝑑
=
𝑏
𝑒
=
𝑐
𝑓
∠𝐵 = ∠𝐷
𝐹
∠𝐶 = ∠𝐹
= 𝑘 (where 𝑘 is the scale factor)
NOTE: The ratio of the areas of two similar triangles is equal to the scale factor squared
𝑨𝒓𝒆𝒂 𝒐𝒇 ∆𝑨𝑩𝑪
= 𝒌𝟐
𝑨𝒓𝒆𝒂 𝒐𝒇 ∆𝑫𝑬𝑭
Example ①
∆𝐶𝐴𝑇~∆𝐷𝑂𝐺. Determine the measure of all sides
𝐴
𝑂
1.5
1
6
𝐶
𝑇
𝐷
8
𝐺
Example ② Identify a pair of similar triangles and explain why they are similar. Support each statement
with a reason. Determine the value of 𝑥.
𝐴
𝒙
𝐷
50 cm
𝐶 20 𝑐𝑚 𝐵
30 m
𝐸
Example③
The triangles below are similar. Determine the unknown side lengths.
A
a)
5 cm
𝑇
°
A
B
×
3 cm
×
B
b)
D
6 cm
C
𝑈
50 m
15𝑐𝑚
°
45 m
𝐹
17m
𝑍
D
15 m
E
Example ③ ∆𝑋𝑌𝑍~∆𝑃𝑄𝑅. Determine the area of ∆𝑃𝑄𝑅.
X
P
12 cm
8 cm
𝐴𝑟𝑒𝑎 = 54 𝑐𝑚2
Y
Z
Q
R