Download JK KL MP

November 29, 2012
6-3 Similar Triangles
Angle-Angle Similarity: (AA
)
*If two angles of one triangle are congruent to two angles of another
triangle, then the triangles are similar.
A
D
B
A
C
=
D
E
and
then
C
ABC
F
=
E
DFE
6-3 Similar Triangles
Side-Side-Side Similarity (SSS
):
*If the measures of the corresponding
sides of two triangles are proportional, the
the triangles are similar.
M
L
N
K
J
JK
MN
JKL
P
KL
NP
JL
MP
MNP
November 29, 2012
6-3 Similar Triangles
Side-Angle-Side Similarity (SAS
):
*If the measures of two sides of one
triangle are proportional to the corresponding
sides of another triangle and the included
angles are congruent, the the triangles are
similar.
T
X
RT
YX
RS
YZ
and
Z
Y
S
R
R= Y
then
RST
YZX
6-3 Similar Triangles
Similarity of triangles is reflexive, symmetric, and transitive:
Reflexive:
Symmetric:
Transitive:
November 29, 2012
6-3 Similar Triangles
Example 1:
In the figure, AB DC. BE = 27, DE = 45,
AE = 21, and CE = 35. Determine which
triangles in the figure are similar.
C
B
E
D
A
6-3 Similar Triangles
R
Example 2:
Given RS UT, RS = 4, UT = 10
RQ = x + 3, QT = 2x + 10, find RQ
and QT.
S
Q
U
T
November 29, 2012
Example 3:
6-3 Similar Triangles
Josh wanted to measure the height of the Sears
Tower in Chicago. He used a 12-foot light pole and
measured its shadow at 1 p.m. The length of the light
poles shadow was 2 feet. Then he measured the
length of the Sears Tower shadow and it was 242 feet
at that time. What is the height of the Sears Tower?