Ellis designed a rectangular envelope using
these measurements. What is w, the width
in centimeters in simplest radical form?
3√7
Figures that are similar (~) have the same
shape but not necessarily the same size.
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!
Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math
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
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.
Determine whether the
RECTANGLES are similar. If so,
write the similarity ratio and a
similarity statement.
Determine whether the
polygons are similar. If
so, write the similarity
ratio and a similarity
statement.
What would be the
similarity shortcuts for
triangles?
Explain why the triangles
are similar and write a
similarity statement.
∆ABC ~ ∆DEF by AA ~
∆DEF and ∆HJK
Verify that the triangles are similar.
D H by the Definition of Congruent Angles.
Therefore ∆DEF ~ ∆HJK by SAS ~.
Verify that the triangles are similar.
∆PQR and ∆STU
Therefore ∆PQR ~ ∆STU by SSS ~.
Explain why ∆ABE ~ ∆ACD, and then find CD.
∆ABE ~ ∆ACD by AA ~.
Given: 3UT = 5RT and 3VT = 5ST
Prove: ∆UVT ~ ∆RST
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?
Homework
• Worksheet