Download Geometry 6.3

Geometry 6.5
SWLT: Use the SSS & SAS Similarity Theorems
Side-Side-Side (SSS) Similarity
Theorem
 If the corresponding side lengths of two triangles are
proportional, then the triangles are similar.
If
AB BC CA
, then ABC  RST
=
=
RS ST TR
A
R
B
C
S
T
Using the SSS Theorem
 Which is Similar to ABC?
D
6
4
A
8
B
E
24
J
9
12
F
8
C
H
16
18
G
Compare the Triangles by finding the
ratios of the corresponding Sides
ABC  DEF?
 Shortest Sides
ABC  GHJ?
 Shortest Sides
AB 8
= =2
DE 4
AB 8 1
= =
GH 16 2
 Longest Sides
 Longest Sides
BC 12 3
= =
EF 8 2
 Remaining Sides
AC 9 3
= =
DF 6 2
 The ratios are not the same, so
ABC is not similar to DEF
BC 12 1
=
=
HJ 24 2
 Remaining Sides
AC 9 1
= =
GJ 18 2
 All ratios are equal, ABC  GHJ
Side-Angle-Side (SAS) Similarity Theorem
 If an angle of one triangle is congruent to an angle of a
second triangle and the lengths of the sides that form these
angles are proportional, then the triangles are similar
If ÐX @ ÐM and
ZX XY
=
PM MN
,
then XYZ  MNP
M
X
N
Y
Z
P
Using SAS… is PRQ  TSR?
 PRQ and SRT are vertical
angles,  are congruent
P
 Find the Ratios of the
corresponding sides
18
 Longer Sides
PR 18 3
=
=
TR 24 4
 The corresponding sides
proportional, so PRQ  TRS
12
R
 Shorter Sides
QR 9 3
=
=
SR 12 4
S
9
Q
24
T