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Lesson 13.2
Similar Triangles
pp. 542-547
Objectives:
1. To identify and illustrate the basic
similarity postulate for triangles.
2. To illustrate, state, and prove the
SSS Similarity Theorem.
3. To identify the SAS Similarity
Theorem.
4. To apply the similarity postulate
and theorems to pairs of triangles
with similarity.
What does ABC ~ XYZ
mean?
C
Z
X
A
B
Y
If ABC ~ XYZ then A  X,
B  Y, C  Z, and
XY
YZ
XZ
=
=
AB
BC
AC
Postulate 13.1
AA Similarity Postulate. If two
angles of one triangle are
congruent to two angles of
another triangle, then the two
triangles are similar.
The AA Similarity Postulate
allows us to say two triangles
are similar if only two pairs of
corresponding angles are
known to be congruent.
Theorem 13.1
SSS Similarity Theorem. If the
three sides of one triangle are
proportional to the
corresponding three sides of
another triangle, then the
triangles are similar.
Theorem 13.2
SAS Similarity Theorem. If two
sides of one triangle are
proportional to the
corresponding two sides of
another triangle and the
included angles between the
sides are congruent, then the
triangles are similar.
Theorem 13.3
Similarity of triangles is an
equivalence relation.
Definition
An equivalence relation is a
relation that is reflexive,
symmetric, and transitive.
Homework
pp. 545-547
►A. Exercises
State whether the lengths (in units) below
could be sides of similar triangles.
1. 3, 8, 7, and 12, 32, 28
►A. Exercises
State whether the lengths (in units) below
could be sides of similar triangles.
3. 12, 15, 9, and 4, 5, 3
►A. Exercises
State whether the lengths (in units) below
could be sides of similar triangles.
5. 7, 4, 9, and 14, 10, 18
►A. Exercises
Which pair of triangles are similar? Why?
7.
►A. Exercises
Which pair of triangles are similar? Why?
9.
6
4
12
8
8
16
►A. Exercises
Which pair of triangles are similar? Why?
11.
►B. Exercises
Prove the following statements.
13. Given: WXYZ is a parallelogram
Prove: WXY ~ YZW
Z
Y
W
X
►B. Exercises
13.
Z
Y
W
X
Statements
Reason
1. WXYZ is a parallel. 1. Given
2. ZY||WX; ZW||YX
2. Def. of Parallel.
3. ZYW  YWX
ZWY  XYW
4. WXY  YZW
3. Parallel Post.
4. AA
■ Cumulative Review
21. What is a relation that is
reflexive, symmetric, and
transitive?
■ Cumulative Review
22. List three symbols that represent
equivalence relations.
■ Cumulative Review
23. Does the set of rotations with a
given center P form an
equivalence relation?
■ Cumulative Review
24. Suppose two regions are related
if they have the same area. Is this
an equivalence relation? Why?
■ Cumulative Review
25. Suppose two solids with the same
volume are related. Is this an
equivalence relation? Why?