Download Honors Geometry Section 8.2 B Similar Polygons

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Transcript
Geometry Section 8.3
Similar Polygons
In very simple terms, two polygons are
similar iff
they have exactly the same shape.
More formally, two polygons are
similar iff their vertices can be paired
so that:
1. corresponding angles are congruent
2. corresponding sides are
proportional.
Note: For corresponding sides to
be proportional, the ratios of the
corresponding sides must be equal.
To state that the polygons to the right are
similar, we might write
ABCDE ~ JFGHI
_______________
or
_______________
CDEAB
~ GHIJF
These statements are called
similarity statements.
List 2 (of the 5) pairs of congruent
angles.
List 5 ratios that will be equal.
A statement such as this is called a
proportionality statement.
Example: In the figure above, AB = 15, JF = 21, FG =
30, GH = 14, DE = 18 and EA = 10. Find all missing
lengths.
AB BC CD DE EA




JF FG GH HI
IJ
15 BC CD 18 10




21 30
14 HI IJ
15 BC CD 18 10




21 30
14 HI IJ
BC  150
21 BC  15  30
7
21 CD  15 14 CD  10
15  HI  2118 HI  25.2
15  IJ  2110 IJ  14
The scale factor of two similar
polygons is the ratio of any pair of
corresponding sides.
For the figures above, the scale factor
is equal to 15 5
21

7
Note: You must write the scale factor in the
same order as the similarity statement.
Example: ABC ~ XYZ and AB = 24, BC = 32 and
YZ = 40. What segment can you find the length of
and what is its length? What is the scale factor for
this similarity?
AB BC AC


XY YZ XZ
24 32 AC


XY 40 XZ
32  XY  960
XY  30
scale factor 
32 4

40 5