Download 9.3 Similar Triangles

9.3 Similar Triangles
Similar Triangles
You will learn to use AA, SSS, and SAS similarity tests for
triangles.
Nothing New!
Similar Triangles
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Similar Triangles
In previous lessons, you learned several basic tests for determining whether
two triangles are congruent. Recall that each congruence test involves only
three corresponding parts of each triangle.
Likewise, there are tests for similarity that will not involve all the parts of
each triangle.
If two angles of one triangle are congruent to two
corresponding angles of another triangle, then the triangles
similar
are ______.
Postulate
9-1
AA Similarity
C
F
A
B
D
If A ≈ D and B ≈ E, then ΔABC ~ ΔDEF
E
Similar Triangles
Two other tests are used to determine whether two triangles are similar.
proportional
If the measures of the sides of a triangle are ___________
to the measures of the corresponding sides of another
triangle, then the triangles are similar.
C
Theorem 9-2
6
2
SSS
Similarity
A
1
8
If
B
D
F
3
4
E
8AB 2 AC6 CB
similar
thentriangles
ΔABC ~ are
ΔDEF
    then the
4
DE 1 DF3 FE
Similar Triangles
proportional
If the measures of two sides of a triangle are ___________
to the measures of two corresponding sides of another triangle
and their included angles are congruent, then the triangles are
similar.
C
Theorem 9-3
SAS
Similarity
2
A
1
8
B
D
F
4
AB8 AC
2
and A  D
If If 
DE4 DF
1
then ΔABC ~ ΔDEF
E
Similar Triangles
Determine whether the triangles are similar.
is used and complete the statement.
If so, tell which similarity test
J
14
G
6
K
9
21
10
H
M
15
P
Since
6
9
=
10
15
Therefore, ΔGHK ~ Δ
=
14
21
JMP
, the triangles are similar by SSS similarity.
Similar Triangles
Fransisco needs to know the tree’s height. The tree’s shadow is 18 feet long
at the same time that his shadow is 4 feet long.
If Fransisco is 6 feet tall, how tall is the tree?
1) The sun’s rays form congruent angles with the
ground.
2) Both Fransisco and the tree form right
angles with the ground.
4
18
=
6
t
4t = 108
t = 27
The tree is
27 feet tall!
6 ft.
4 ft.
18 ft.
Similar Triangles
Slade is a surveyor.
To find the distance across Muddy Pond,
he forms similar triangles and measures
distances as shown.
What is the distance
across Muddy Pond?
10
45
=
8
x
10x = 360
x = 36
45 m
x
8 m
10 m
It is 36 meters across Muddy Pond!
Summary:
3 ways to prove that 2 triangles are
similar:
AA, SSS, SAS
Similar Triangles