Theorems for Similar Triangles
Lesson 7.5
Pre-AP Geometry
Lesson Focus
Two theorems for showing that two triangles are similar are
presented in this lesson.
These theorems, along with the definition of similarity and
the AA Similarity Postulate, provide four ways to prove that
two triangles are similar.
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of another
triangle and the sides including those angles are in
proportion, then the triangles are similar.
Triangle ABC is similar to triangle DEF because A and D are
congruent and AB:DE = AC:DF.
SSS Similarity Theorem
If the sides of two triangles are in proportion, then the
triangles are similar.
AB:DE = AC:DF = BC:EF
The two triangles are similar
SAS/SSS Similarity Theorems
Example 1: The measures of the sides of ABC are 4, 5, and 7
and the measures of the sides of XYZ are 16, 20, and 28. Are
the triangles similar?
Example 2: In ABC, AB = 2, AC = 5, and BC = 6. In XYZ, XY =
2.5, YZ = 2, and XZ = 3. Is ABC XYZ?
SAS/SSS Similarity Theorems
Example 3: Name similar triangles and give the postulate or
theorem that justifies your answer.
A
D
80
E
80
B
C
SAS/SSS Similarity Theorems
Example 4: Name similar triangles and give the postulate or
theorem that justifies your answer.
C
6
D
3
A
10
E
5
B
SAS/SSS Similarity Theorems
Example 5: Name similar triangles and give the postulate or
theorem that justifies your answer.
L
3
5
6
K
M
6
6
10
O
N
SAS/SSS Similarity Theorems
Example 6: If ABC  DEF, does AB correspond to DE ?
Does BC correspond to EF ?
Does AC correspond to DF ?
SAS/SSS Similarity Theorems
A
Example 7: Given: B  DEC
Prove: ABC  DEC
Proof:
Statements
D
B
Reasons
E
C
Similar Triangles
Remember, you must match corresponding vertices when
naming similar triangles.
Similar Triangles
Ways to prove triangles similar:
– Definition of Similarity
– AA Similarity Postulate
– SAS Similarity Theorem
– SSS Similarity Theorem
Written Exercises
Problem Set 7.5, p.266: # 2 - 12 (even); Handout 7-5