Download Contraction Expansion

Unit 7
Unit 7
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M.Sigley, SSI MS
Unit 7
M.Sigley, SSI MS
Contraction
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Unit 7
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Scale Factor
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Expansion
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Unit 7
DEFINITION
DEFINITION
Unit 7
Dilation
Scale Factor
 Transformation that is not
 The ratio of two
corresponding lengths
rigid
 Same shape, different size
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Unit 7
DEFINITION
Expansion
Unit 7
DEFINITION
Contraction
 A dilation with a scale factor
 A dilation with a scale factor of
less than 1 but greater than 0
greater than 1
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Unit 7
Similarity
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Unit 7
POSTULATE
AA~
Similarity
 Each pair of corresponding angles are
 If two corresponding angles of one
triangle are congruent to two
corresponding angles of another
triangle then the triangles are
similar.
congruent
 Each pair of corresponding sides are
proportional
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POSTULATE
Unit 7
SAS~
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M.Sigley, SSI MS
POSTULATE
Unit 7
SSS~
 If two sides of a triangle are
proportional to two sides of another
triangle and the included angle of
that triangle is congruent to the
included angle of the other triangle,
then the triangles are similar.
M.Sigley, SSI MS
POSTULATE
Unit 7
 If the corresponding sides of one
triangle are proportional to the
corresponding sides of another
triangle then the triangles are
similar.
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THEOREM
Proportional Altitudes
Side Splitter
If two triangles are similar then their
altitudes have the same ratio as their
corresponding sides.
A line parallel to one side of the
triangle divides the other two sides
proportionally.
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THEOREM
Proportional Angle Bisectors
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THEOREM
Proportional Medians
If two triangles are similar then their
angle bisectors have the same ratio as
their corresponding sides.
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THEOREM
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If two triangles are similar then their
medians have the same ratio as their
corresponding sides.
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Unit 7
Area Ratio
Proportional Segments
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Cylinder A
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s.wikimedia.org/wiki/File:Golden_rectan...
Cylinder B
Cylinder A is similar to Cylinder B
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Unit 7
Volume Ratio
Unit 7
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Unit 7
FORMULA
Ratio of Area of Similar Figures
Proportional Segments
Two similar figures with corresponding
side measures in the ratio of
a/b have
2
areas in ratio a
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THEOREM
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/b2.
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FORMULA
An angle bisector of a triangle divides
the opposite side into two segments
that have the same ratio as the other
two sides.
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FORMULA
Ratio of Volume of Similar Figures
Golden Rectangle
Two similar solids with corresponding
a/b have
3 3
volumes in ratio a /b .
side measures in the ratio of
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