Use Theorems to Prove Triangle Similarity
Determine if you can prove if each pair of triangles is similar. If so, state the theorem that you can use to prove it
and the similarity statement. If you can’t prove it, state either not similar or not enough information.
1.
E
Since the lines are parallel, you can use AA to prove they are similar.
Angle ABC and angle EDF are corresponding because they are on
parallel lines cut by a transversal. Angle ACB and angle EFD are also
corresponding.
A
B
D
F
C
B
2.
A
36 divided by 12 is 3. 45 divided by 15 is 3. Since
these have the same ratio and the angle between
them is marked, you can use SAS to prove similarity.
E
C
15
D
F
45
B
3.
A
15 divided by 5 is 3. 20 divided by 7 is not 3. Since
these have different ratios, they are not similar.
E
C
7
D
F
20
Since the angle is not between the sides on triangle
JKL, you cannot use SAS to prove they are similar.
The angle must be between the two marked sides.
You cannot use AA because only one angle is marked.
You cannot use SSS because only two sides are
marked. There is not enough information to prove
or disprove similarity.
F
4.
J
H
G
L
21
K
8
F
5.
Angle FDE is 130 degrees and angle FBC is 130
degrees. Angle F would be congruent to itself. This
gives you two congruent angles so you can use AA to
prove similarity.
D
130°
E
C
130°
B
Each side is multiplied by 10 to
get the new sides. This means
that all three sides are
proportional so you can use SSS
to prove similarity.
D
A
6.
5
4
B
6
50
40
C
E
X
60
F
R
7.
Z
100°
Y
S
T
For this one, you can’t prove it
with what is marked, but if you
do a little math you can. Since
the two marked angles in XYZ
are 100 and 40, the third one
must be 40. This gives you two
40 degree angles in each
triangle so you can use AA to
prove similarity.