ellis designed a rectangular envelope using these...
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Ellis designed a rectangular envelope using
these measurements. What is w, the width
in centimeters in simplest radical form?
3√7
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Figures that are similar (~) have the same
shape but not necessarily the same size.
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Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.
Oh look- a fancy box!
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Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math
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Identify the pairs of congruent angles
and corresponding sides. Name the
similar triangles.
N Q and P R.
By the Third Angles Theorem, M T.
0.5
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A similarity ratio is the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is , or .
The similarity ratio of ∆DEF to ∆ABC is , or 2.
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Determine whether the
RECTANGLES are similar. If so,
write the similarity ratio and a
similarity statement.
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Determine whether the
polygons are similar. If
so, write the similarity
ratio and a similarity
statement.
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What would be the
similarity shortcuts for
triangles?
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Explain why the triangles
are similar and write a
similarity statement.
∆ABC ~ ∆DEF by AA ~
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∆DEF and ∆HJK
Verify that the triangles are similar.
D H by the Definition of Congruent Angles.
Therefore ∆DEF ~ ∆HJK by SAS ~.
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Verify that the triangles are similar.
∆PQR and ∆STU
Therefore ∆PQR ~ ∆STU by SSS ~.
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Explain why ∆ABE ~ ∆ACD, and then find CD.
∆ABE ~ ∆ACD by AA ~.
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Given: 3UT = 5RT and 3VT = 5ST
Prove: ∆UVT ~ ∆RST
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You learned in Chapter 2 that the Reflexive,
Symmetric, and Transitive Properties of Equality
have corresponding properties of congruence. Do
these properties also hold true for similarity of
triangles?
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Homework
• Worksheet