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Geometry
Sections 6.4-6.5
Proving Triangles Similar
Remember that triangles which are similar have congruent corresponding angles and
corresponding sides which are proportional.
You should be able to write a proportionality statement for a pair of similar triangles and use
that statement to find any missing sides.
Ex 1)
LMN
PQN
33
L
M
A. Write a proportionality statement for the figures.
106
N
B. Find the measures of angles M and P.
20
C. Find MN and QM
Q
36
P
30
There are three ways to prove triangles similar:
Postulate 22 Angle-Angle Similarity (AA) If two angles of a triangle are congruent to two
angles of another triangle, then the triangles are similar.
Theorem 6.2 Side-Side-Side Similarity (SSS) If all pairs of corresponding sides of two
triangles are proportional, then the triangles are similar.
Theorem 6.3 Side-Angle-Side Similarity (SAS) If an angle of one triangle is congruent to
an angle of another triangle and the lengths of the sides including these angles
are proportional, then the triangles are similar.
2) A building casts a shadow 26 ft long. At
the same time of day, a person 71 inches
tall casts a 48 inch shadow. How tall is
the building?
1) Identify any similar triangles.
Q
44 R
P
44 T
S
3) What value of x makes the triangles
similar?
20
12
x6
30
15
21
30
21
3  x  2
4) Are any of the triangles similar?
30
20
15
21
35
42