Triangle Similarity Using SSS and SAS

1. 5-5
SSS & SAS

2. Proving Triangles
Congruent

3. TThhee IIddeeaa ooff aa CCoonnggrruueennccee
Two geometric figures with exactly the same size and shape.
B
A C
F
E D

4. HHooww mmuucchh ddoo yyoouu
nneeeedd ttoo kknnooww.. .. ..
. . . about two triangles
to prove that they
are congruent?

5. CCoorrrreessppoonnddiinngg PPaarrttss
You learned that if all six pairs of
corresponding parts (sides and angles)
are congruent, then the triangles are
congruent.
B
A C
DABC @ D
DEF
E
D F
1. AB @ DE
2. BC @ EF
3. AC @ DF
4. Ð A @ Ð D
5. Ð B @ Ð E
6. Ð C @ Ð F

6. Side-Side-Side (SSS) Similarity Theorem
If the corresponding side lengths of two triangles are
proportional, then the triangles are similar.

7. SSiiddee--SSiiddee--SSiiddee ((SSSSSS))
1. AB @ DE
2. BC @ EF
3. AC @ DF
DABC @ D DEF
B
A C
E
D F

8. Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of a
second triangle and the lengths of the sides including
these angles are proportional, then the triangles are
similar.

9. SSiiddee--AAnnggllee--SSiiddee ((SSAASS))
1. AB @ DE
2. ÐA @ Ð D
3. AC @ DF
DABC @ D DEF
B
A C
E
D F
included
angle

10. Slide 1 of 2

11. IInncclluuddeedd AAnnggllee
The angle between two sides
Ð G Ð I Ð H

12. IInncclluuddeedd AAnnggllee
Name the included angle:
YE and ES
ES and YS
YS and YE
E
Y S
Ð E
Ð S
Ð Y

13. NNaammee TThhaatt PPoossttuullaattee
SSAASS
(when possible)
SSSSAA SSSSSS

14. NNaammee TThhaatt PPoossttuullaattee (when possible)
Reflexive
SSAASS
SSAASS SSAASS
Property
Vertical
Angles
Vertical
Angles
Reflexive
Property SSSSAA

15. Write a congruence statement for each
pair of triangles represented.
A
B
F
C
E
D

16. Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove that they
are congruent, write not possible.
ΔACB @ ΔECD by
SAS
B
A
C
E
D
Ex 6

17. Slide 2 of 2

18. Slide 2 of 2

19. Slide 2 of 2

20. (over Lesson 5-5)
Slide 1 of 2

21. (over Lesson 5-5)
Slide 1 of 2