Similar Triangles
Similar Triangles
Similar Triangles
SIMILAR TRIANGLES
How can we know similar figures?
If two figures are similar, one figure is an
enlargement of the other. The scale factor tells the
amount of enlargement or reduction.
Original Copy
Original Copy Original Copy
Exact Copy
Enlargement Reduction
Copy machine set to 100%
Copy machine is set to 200% Copy machine is set to 50%
Scale Factor is 1:1
Scale Factor is 1:2 Scale Factor is 2:1
Similar figures have the same shape but not
necessarily the same size.
• The ~ symbol means “is similar to”
Two polygons are similar polygons if:
CORRESPONDING ANGLES ARE
CONGRUENT and if the lengths of
CORRESPONDING SIDES ARE
PROPORTIONAL.
E
A ΔABC ~ ΔEFG
F G
B C
Angles
Sides
∠A ≅ ∠ E
∠B ≅ ∠ F
==
∠C ≅ ∠ G
U N D E R S TA N D I N G S I M I L A R I T Y
MNP ~ SRT
What are the pairs of congruent angles?
∠M ≅ ∠ S, ∠N ≅ ∠ R, ∠P ≅ ∠ T
What is the extended proportion for the ratios of
corresponding sides? ==
the ratio of corresponding linear
T O R
L E FA C measurements of two similar figures.
SC A
ABC to XYZ ==
==
𝟓 𝟓 𝟓
¿ ¿
𝟓𝟐 𝟐 𝟐
𝒔𝒄𝒂𝒍𝒆 𝒇𝒂𝒄𝒕𝒐𝒓 𝒊𝒔 𝟓 :𝟐 𝒐𝒓
𝟐
a m pl e
Ex
𝒀𝑬𝑺
Are the polygons similar?
write a similarity statement
J P
H O
<J comp. <K <K = 50 <H = <O
<K = <M 90= y
50 = x + 5
180 = y
45 = x
xa m pl e
E
Decide if the triangles M
are similar. 10.5
P
4
18
L 12 Q
not similar. R
N
a m pl e
Ex
Find the value of x, y, and the
measure of P if TSV ~ QPR.
y = 10.5
x=6 P = 86°
xa m pl e
E
USING SIMILARITY
In the diagram, find .
PS PT
.
PR PQ
=
= =