Similarity in Triangles
Side-Side-Side Similarity Postulate (SSS)
If the corresponding sides of two
triangles are proportional, then
the triangles are similar.
Similarity in Triangles
Side-Side-Side Similarity Postulate (SSS)
If the corresponding sides of two triangles are
proportional, then the triangles are similar.
6
8
4
3
A
9
12
Check by cross
multiplying
24 = 24
B
=
=
72 = 72
A  B because
of the SSS
Postulate.
Similarity in Triangles
Side-Side-Side Similarity Postulate (SSS)
If the corresponding sides of two triangles
are proportional, then the triangles are similar.
12
4
A
8
B
16
8
6
=
48 = 48
=
96 = 96
A  B because of
the SSS Postulate.
Similarity in Triangles
Side-Side-Side Similarity Postulate (SSS)
If the corresponding sides of two triangles are
proportional, then the triangles are similar.
21
5
B
A
15
7
18
=
126 = 126
=
90 = 90
6
A  B because
of the SSS
Postulate.
Similarity in Triangles
If two angles of one triangle are congruent to two
angles of another triangle, what does that tell us?
We know the sum of 40°
the angles of a
triangle is 180°
180⁰ – (65°+40⁰) =
65°
40°
We know the sum of the
angles of a triangle is 180°
B
A
65°
180⁰ – (65°+40⁰) =
75°
75°
So, if 2 angles are congruent, the 3rd must be also
We know if 3 angles are congruent, the triangles are similar
So…..
Similarity in Triangles
Angle-Angle Similarity Postulate (AA)
If two angles of one triangle are
congruent to two angles of
another triangle, then the
triangles are similar.
Similarity in Triangles
Angle-Angle Similarity Postulate (AA)
If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are
similar.
50°
B
A
70°
70°
50°
A  B because of
the AA~ Postulate.
Similarity in Triangles
Angle-Angle Similarity Postulate (AA)
If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are
similar.
50°
B
A
50°
A  B because of
the AA~ Postulate.
Similarity in Triangles
Angle-Angle Similarity Postulate (AA)
If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are
similar.
A
Vertical angles are
congruent
B
A  B because of
the AA~ Postulate.
Similarity in Triangles
Side-Angle-Side Similarity Postulate (SAS)
If an angle of one triangle is
congruent to an angle of another,
and the two sides that make the
angle are proportional, then the
triangles are similar.
Similarity in Triangles
Side-Angle-Side Similarity Postulate (SAS)
If an angle of one triangle is congruent to an angle of another,
and the two sides that make the angle are proportional, then
the triangles are similar.
4
A
50⁰
6
B
6
50⁰
=
36 = 36
9
A  B because of
the SAS Postulate.
Similarity in Triangles
Side-Angle-Side Similarity Postulate (SAS)
If an angle of one triangle is congruent to an angle of another,
and the two sides that make the angle are proportional, then
the triangles are similar. B
2
6
A
3
4
=
12 = 12
A  B because of
the SAS Postulate.
Are the following triangles similar?
If so, name the theorem you used.
G
M
3
6
O
H
4
I
R
8
=
Yes they are similar SAS
Are the following triangles similar?
If so, name the theorem you used.
A
This angle is used
for both, so it is
congruent to itself
5
5
25
Y
X
4
4
B
C
=
Yes they are similar SAS
Are the following triangles similar?
If so, name the theorem you used.
A
This angle is used for both,
so it is congruent to itself
X
Y
B
Yes they are similar AA
C
Are the following triangles similar?
If so, name the theorem you used.
A
This angle is used for both,
so it is congruent to itself
Y
B
70⁰
110⁰ 70⁰
X
Supplementary
angles add to 180⁰,
so this angle is
C
Yes they are similar AA
Are the following triangles similar?
If so, name the theorem you used.
10
18
12
15
=
Yes they are similar SAS
Vertical angles
are congruent