Transcript Similarity Theorems for Triangles

Similarity Tests
for Triangles
Angle Angle Similarity
Postulate ( AA~)
S
Y
X
Z
R
T
X  R and Y  S
Therefore,  XYZ ~ RST by AA~
Side-Side-Side Similarity
Theorem ( SSS~)
P
W
3
Put the three sides from
one triangle
4 in order on
10.5
top.
X
V
12
Put the three sides from
the other triangle in
order on bottom.
3 10.5 12


4
14 16
.75  .75  .75
R
14
16
Q
Therefore,
 WXV ~ PRQ by SSS~
Divide out each ratio and see
if all three are the same. If
so, the triangles are similar.
Side-Angle-Side Similarity
Theorem ( SAS~)
First, make sure you
have a pair of
P
corresponding angles
congruent.
W
4
3
X
12
Put the two sides from
one triangle that form
that angle in order on top.
V
R
3 12

4 16
.75  .75
X  R
16
Put the two sides from the
Divide out each ratio
other triangle forming the
and see if both are the
angle in order on bottom.
same. If so, the
triangles are similar.
Q
Therefore,
 WXV ~ PRQ by SAS~
E xamples
What parts do you
know?
Test for
SSS~.
6
10
15
18
25
30
.6 = .6
= .6
Yes!
KML ~QSR
by SSS~
E xamples
Now, What do
You know vertical
1st, write given
info on the figure.
6
you know?
angles
Next, are
youcongruent,
know the
so sides
markthat
them.
two
form
AC + CD = AD
for
6the
+ CDangles….check
= 10
CD = 4
SAS!
BC + CE = BE
9 + CE = 15
CE = 6
4
4
6
6
9
.6rep = .6rep
Yes!
DCE ~ACB
by SAS~