Download 8.5 Proving Triangles are Similar



Use similarity theorems to prove
that two triangles are similar
Use similar triangles to solve reallife problems

If the corresponding sides of two
triangles are proportional, then the
triangles are similar.
P
A
B
C
AB BC CA


PQ QR RP
Q
R
THEN ∆ABC ~ ∆PQR

X
If an angle of one triangle is congruent to an
angle of a second triangle and the lengths of
the sides including these angles are
proportional, then the triangles are similar.
M
Z
Y
P
N
ZX
XY
If ÐX @ÐM and
=
,
PM
MN
then
VXYZ : VMNP
SSS Similarity Theorem
S
65°
18
T
24
SAS
Similarity
Theorem
U
J
6
K
65°
8
L