triangle congruence

2. The Idea of a Congruence
Two geometric figures
with exactly the same size
and shape. F
B
A C
E D

3. Congruent figures can be rotations of one another.

4. Congruent figures can be reflections of one another.

5. How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?

6. Corresponding Parts
We learned that if all six pairs of
corresponding parts (sides and angles) are
congruent, then the triangles are congruent.

7.  In proving the congruency of two
triangles, we do not need all the six
corresponding parts but only 3 parts.
Either the three sides, two sides and
one angle or two angles and one side.

8. Side-Side-Side (SSS)
Two triangles are congruent if all the
three sides of one triangle are equal to
the three sides of other triangle.

9. Side-Angle-Side (SAS)
• AB ≅ DE
• ∠A ≅ ∠D
• AC ≅ DF
∆ABC ≅ ∆DEF
included
angle
Two triangles are congruent if any two sides and the includes angle of
triangle is equal to the two sides and the included angle of other triangle.

10. Included Angle
The angle between two
sides

11. Included Angle
Name the included angle:
YE and ES
ES and SY
SY and YE

12. Angle-Side-Angle (ASA)
• ∠ A ≅ ∠ D
•
∠ B
≅
∠ E
•
BC
≅
EF ∆ABC ≅ ∆ DEF
Included Side
Two triangles are congruent if two angles and the included side of one
triangle are congruent to two angles and the included side of
another triangle.

13. Included Side
The side between two angles
GI HI GH

14. E
Y S
Included Side
Name the included side:
ZY and ZE YE
ZE and ZS ES
ZS and ZY SY

15. Angle-Angle-Side (AAS)
• ∠ A ≅ ∠ D
• ∠ B ≅ ∠ E
• BC ≅ EF
∆ABC ≅ ∆DEF
Non-included
side
Two triangles are congruent if two angles and a non-included side of
one triangle are congruent to two angles and a non-included side of
another triangle.

16. Warning: No SSA Postulate
B E
NOT CONGRUENT
F
There is no such
thing as an SSA
postulate!

17. Warning: No AAA Postulate
NOT CONGRUENT
B
E
There is no such
thing as an AAA
postulate!
A C D
F

18. The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
ndence
dence

19. NAME THE POSTULATE

21. Name That Postulate
(when possible)
Reflexive
Property
Vertical
Angles
Vertical Angles
Reflexive
Property

22. I. Let’s Practice
Name That Postulate
1.
4.
3.
2.

23. 5.
6.
7.

24. II. Let’s Practice
1. Indicate the additional information
needed to enable us to apply the specified
congruence postulate.

25. 2. Indicate the additional information
needed to enable us to apply the specified
congruence postulate.
For ASA:
For SAS:
For AAS:

26. 3. 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.
G K

27. 4. 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.
B A
C
E

28. 5. 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.
C
B A
E
D

29. 6. 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.

30. 7. Determine if whether each pair of triangles are
congruent by SSS, SAS, ASA, or AAS. If not possible to prove
that they are congruent, write notpossible.
J
L
T