Download Use Similar Polygons (6

Use Similar () Polygons (6.3)
Same Shape Different Size!
Definition: Two Polygons are Similar Polygons if:
1. corresponding angles are congruent and
2. corresponding side lengths are proportional. (ratios are  )
In the diagram below ABCD  EFGH
F
B
C
A
Ex.
Ex.
G
D
E
H
List the corresponding angles:
A  _________
C  _________
B  _________
D  _________
Write the ratio of corresponding sides:
AB

BC

CD

AD
Definition: If two polygons are similar, the Scale Factor is the
ratio of the lengths of any two corresponding sides.
Ex. Find the scale factor of the similar polygons below
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Determine whether the polygons below are similar.
If they are write a similarity statement and find the scale factor.
Remember:
1. corresponding angles must be congruent &
2. ratios of corresponding sides must reduce to the same fraction.
Ex.
Ex.
In the diagram, DEF MNP
N
E
Ex. Find the value of x
x
9
D
12
20
12
F
M
16
P
Ex. Find the scale factor of DEF to MNP
Ex. Perimeter of DEF = ___________ and Perimeter of MNP = __________
Ex. Find the ratio of the perimeter of DEF to the perimeter of MNP.
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Theorem 6.1
Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is equal to the
ratios of their corresponding side lengths (which is the scale factor).
If CDEF ~ MJKL, then
In the diagram, WXYZ  MNOP.
Ex. Find the value z.
Ex. Find the values of x & y.
Find x
Find y
Ex. Find the scale factor of WXYZ to MNOP.
Ex. Find the perimeter of WXYZ and the perimeter of MNOP.
Ex. Find the ratio of the perimeter WXYZ of to the perimeter of MNOP.
Note: Should be the same answer as the scale factor!
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Corresponding Lengths in Similar Polygons
If two polygons are similar, then the ratio of any two corresponding lengths
in the polygon is equal to the scale factor of the similar polygons



The altitude of one triangle is in proportion to the corresponding altitude of the other triangle.
The median of one triangle is in proportion to the corresponding median of the other triangle.
The perpendicular bisector of one triangle is in proportion to the corresponding perpendicular
bisector of the other triangle
In the diagram below, ABC EC
A
D
G
F
C
E
B
Ex. CF and CG are _______________________ of the triangles
Ex. Find m
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