The document explains the triangle similarity theorems including AA, SAS, and SSS, detailing how to determine if two triangles are similar based on their angles and sides. It provides examples and practice questions to reinforce understanding of these theorems. The document emphasizes the importance of angle congruence and proportional sides in establishing similarity between triangles.

1. TRIANGLE SIMILARITY
THEOREM

2. Proves the SAS and SSS
Similarity Theorems of similar
triangles.
1
Apply the theorems to show that a
given pair of triangles are similar.
2
Show patience in applying the SAS and
SSS Similarity Theorems in two
triangles.
3
LEARNING OBJECTIVES

3. If two angles of one
triangle are congruent to
the corresponding
angles of another
triangle, then the
triangles are similar.
AA Similarity Theorem

4. Example of AA Similarity Theorem
Given:
Prove: ΔABC ~ ΔXYZ..
70 70
30
30
Since the corresponding angles and are both . Also, the
corresponding angles and are both Then, Therefore ΔABC ~
ΔXYZ

5. Example of AA Similarity Theorem
If the triangle are similar, write a similarity
statement between each pair of triangles.

6. Example of AA Similarity Theorem
NO SIMILARITY
Since m and , only
one pair of triangles
are that is

7. Example of AA Similarity Theorem
ΔABC ~ ΔXYZ
Since m m ; by AA
Similarity Theorem,
the triangles are
similar.

8. Example of AA Similarity Theorem
ΔMNO ~ ΔQRP
m m

9. If the corresponding
sides of one triangles
are proportional to the
corresponding sides of
the other triangle, then
the triangles are similar.
SSS Similarity Theorem

10. Example of SSS Similarity Theorem
The common ratio is

11. Example of SSS Similarity Theorem
The common ratio is

12. Example of SSS Similarity Theorem
The common ratio is

13. SAS Similarity Theorem
If two sides of one triangle
are proportional to the
corresponding two sides of
another triangle and the
respective included angles
are congruent, then the
triangles are similar.

14. Example of SAS Similarity Theorem
0
and 0

15. Example of SAS Similarity Theorem
0
and 0

16. Any Question?

17. Clarification?

18. It’s your turn to
answer

19. Choose the letter of the correct
answer!
1. What triangle similarity theorem states that
“If two angles of one triangle are congruent to
the corresponding of another triangle, Then the
triangles are similar.”?
A. AA similarity theorem
D. SSS similarity theorem
C. ASA similarity theorem
B. SAS similarity theorem

20. Choose the letter of the correct
answer!
2. What triangle similarity theorem states that
“If the corresponding sides of one triangles are
proportional to the corresponding sides of the
other triangle, then the triangle are similar.”?
A. AA similarity theorem
D. SSS similarity theorem
C. ASA similarity theorem
B. SAS similarity theorem

21. Choose the letter of the correct
answer!
3. What triangle similarity theorem states that
“If two sides of one triangle are proportional to
the corresponding two sides of another triangle
and the respective included angles are
congruent, then the triangles are similar.”?
A. AA similarity theorem
D. SSS similarity theorem
C. ASA similarity theorem
B. SAS similarity theorem

22. Choose the letter of the correct
answer!
4. What is the similarity
theorem proves that , from
the given figure?
A. AA similarity theorem
D. SSS similarity theorem
C. ASA similarity theorem
B. SAS similarity theorem

23. Choose the letter of the correct
answer!
5. What similarity
theorem is evident in
the given figure on the
right?
A. AA similarity theorem
D. SSS similarity theorem
C. ASA similarity theorem
B. SAS similarity theorem

24. Answer key!
1.A
2.D
3.B
4.B
5.A

25. GOODJOB!