2. SIMILAR FIGURES
Two polygons are similar if and only
if, their corresponding angles are
congruent and the measures of
their corresponding sides are
proportional
7cm
6cm
4cm
8 cm
3cm
2cm
3.5cm
3. Definition: Similar polygons are
polygons in which:
1.The ratios of the measures of
corresponding sides are equal.
2.Corresponding angles are
congruent.
4. SIMILAR FIGURES
The symbol “~” is read as “similar
to”.
Consider the figure below
7cm
6cm
4cm
8 cm
3cm
2cm
3.5cm
6. Proving shapes similar:
1. Similar shapes will
have the ratio of all
corresponding sides
equal.
2. Similar shapes will
have all pairs of
corresponding angles
congruent.
7. When you compare the
lengths of corresponding
sides of similar figures, you
usually get a numerical
ratio. The ratio is called the
scale factor for the two
figures
Scale Factors
8. When finding the scale
factor for two similar
polygons, the scale factor
will depend on the order of
comparison.
9. Example:
A
C
B
D
E F
6
4
8
5 10
12
∆ABC ~ ∆DEF
Therefore: A corresponds to D, B corresponds
to E, and C corresponds to F.
1. The ratios of the measures of all pairs of
corresponding sides are equal.
AB
DE = 2
1 AC
DF 2
1 BC
EF 2
1
= =
10. Each pair of corresponding angles
are congruent.
<B <E <A <D <C <F
11. Given: ABCD ~ EFGH, with measures
shown.
1. Find FG, GH, and EH.
A
B
D
C
G
F
E
H
6
7
4
3
9
2. Find the ratio of the
perimeter of ABCD to the
perimeter of EFGH.
FG =
GH =
EH =
6
4.5
10.5
PABCD = 20
PEFGH = 30
= 2
3
