Transcript Lesson 8.4 Similar Triangles

I
can use triangle similarity
to solve unknown sides and
angles.
 Similar
– two shapes are similar if
they have the same number of
sides, the same number of angles,
and the same angle measure.
Similar triangles are triangles that have the same
shape but not necessarily the same size.
A
D
E
B
ABC  DEF
C
F
A  D
B  E
C  F
AB
DE
=
BC
EF
=
AC
DF
Six of those statements are true as a result of the
similarity of the two triangles. However, if we need to
prove that a pair of triangles are similar how many of
those statements do we need? Because we are
working with triangles and the measure of the angles
and sides are dependent on each other, we do not
need all six. There are three special combinations
that we can use to prove similarity of triangles.
1. SSS Similarity Theorem
 3 pairs of proportional sides
2. SAS Similarity Theorem
 2 pairs of proportional sides and
congruent angles between them
3. AA Similarity Theorem
 2 pairs of congruent angles
E
1. SSS Similarity Theorem
 3 pairs of proportional sides
A
9.6
5
B
C
12
mAB

mDF
mBC

mFE
5
 1.25
4
12
 1.25
9.6
F
4
mAC
13

 1.25
mDE 10.4
ABC  DFE
D
2. SAS Similarity Theorem
 2 pairs of proportional sides and
congruent angles between them
L
G
70
H
7
I
mGH
5

 0.66
7 .5
mLK
mHI
7

 0.66
mKJ 10.5
70
J
10.5
mH = mK
GHI  LKJ
K
The SSA Similarity Theorem does not work. The
congruent angles should fall between the
proportional sides (SAS). For instance, if we have
the situation that is shown in the diagram below, we
cannot state that the triangles are similar. We do
not have the information that we need. L
G
50
H
7
I
J
50
10.5
K
Angles I and J do not fall in between sides GH and HI
and sides LK and KJ respectively.
3. AA Similarity Theorem
 2 pairs of congruent angles
Q
M
70
50
N
mN = mR
mO = mP
O
50
70
P
MNO  QRP
R
It is possible for two triangles to be similar when
they have 2 pairs of angles given but only one of
those given pairs are congruent.
T
X
Y
34
34
59
59
Z
87 59
U
S
mS = 180- (34 + 87)
mS = 180- 121
mS = 59
mT = mX
mS = mZ
TSU  XZY

Work with your partner. Only one paper
per partner.
› Page 483 #10-26 and 40-46 (EVEN # ONLY)
› Page 492 #2- 14 (EVEN # ONLY)

www.dictionary.com
 paccadult.lbpsb.qc.ca/eng/extra/img/S
imilar%20Triangles.ppt
 www.mente.elac.org/presentations/sim_
tri_I.pps
