1. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:

2. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT

3. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT
Prove COORESPONDING SIDES are CONGRUENT
(SSS)

4. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT
Prove COORESPONDING SIDES are CONGRUENT
(SSS)
Prove Two CORRESPONDING Angles and the
INCLUDED SIDE are CONGRUENT (ASA)

5. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT
Prove COORESPONDING SIDES are CONGRUENT
(SSS)
Prove Two CORRESPONDING Angles and the
INCLUDED SIDE are CONGRUENT (ASA)
Prove Two CORRESPONDING Sides and the
INCLUDED ANGLE are CONGRUENT (SAS)

6. GEOMETRY 4.5
Recall: To Prove Triangles are CONGRUENT:
Prove CORRESPONDING Sides and
CORRESPONDING Angles are CONGRUENT
Prove COORESPONDING SIDES are CONGRUENT
(SSS)
Prove Two CORRESPONDING Angles and the
INCLUDED SIDE are CONGRUENT (ASA)
Prove Two CORRESPONDING Sides and the
INCLUDED ANGLE are CONGRUENT (SAS)
????

7. GEOMETRY 4.5 G N
Given:
N  D
G  I
AN = SD S A
Prove:
ANG  SDI D I  

8. GEOMETRY 4.5
THEOREM: (AAS)
If TWO ANGLES and a NONIncluded SIDE of One Triangle
are CONGRUENT to
the CORRESPONDING TWO ANGLES and SIDE of a
Second Triangle,
THEN
the TWO TRIANGLES are CONGRUENT.

9. GEOMETRY 4.5 S T
Given:
PSU  PTR
SU = TR R U
Prove: P

10. GEOMETRY 4.5
Prove:
Given:

11. GEOMETRY 4.5
Given:
Prove:

12. GEOMETRY 4.5
Given:
E is Midpoint
Prove:

13. GEOMETRY 4.5
Given:
Prove:

16. GEOMETRY 4.5
GEOMETRY 4.5
Summary of Congruency Proof Tools
Postulates & Theorems that PROVE Congruency:
Postulates/Theorems that DO NOT Prove Congruency:

17. A SONG about CONGRUENCE

18. C - P - CTC is a Theorem in Geometry

19. C - P - CTC is a Theorem in Geometry
C - P - CTC proves Congruence Easily

20. C - P - CTC is a Theorem in Geometry
C - P - CTC proves Congruence Easily
Get S-S-S A-S-A
S-A-S or S-A-A

21. C - P - CTC is a Theorem in Geometry
C - P - CTC proves Congruence Easily
Get S-S-S A-S-A
S-A-S or S-A-A
C - P - CTC follows immediately

22. GEOMETRY 4.5

24.  SIDES Base ’s THEOREM:
GEOMETRY 4.6
 SIDES Base ’s THEOREM:
If TWO SIDES of a Triangle are CONGRUENT,
THEN
The ANGLES OPPOSITE those SIDES are CONGRUENT.

25.  SIDES Base ’s THEOREM:
GEOMETRY 4.6
 SIDES Base ’s THEOREM: Q
Given:
Prove: P R

26. Triangle ISO is isosceles with base SO. mS = 5x – 18 mO = 2x + 21
GEOMETRY 4.6 S O
Triangle ISO is isosceles
with base SO.
mS = 5x – 18
mO = 2x + 21
m S =
m O =
m  I = I

27. Triangle DEF is isosceles mE = 2x + 40 mF = 3x + 22 m D = m E =
GEOMETRY 4.6 D
Triangle DEF is isosceles
mE = 2x + 40
mF = 3x + 22
m D =
m E =
m F = E F

28. Base ’s  SIDES THEOREM:
GEOMETRY 4.6
Base ’s  SIDES THEOREM:

29. Base ’s  SIDES THEOREM:
GEOMETRY 4.6
Base ’s  SIDES THEOREM:
If TWO ANGLES of a Triangle are CONGRUENT,
THEN
The SIDES OPPOSITE those ANGLES are CONGRUENT.

30. Base ’s  SIDES THEOREM:
GEOMETRY 4.6
Base ’s  SIDES THEOREM: Q
Given:
Prove: P R

31. Equilateral Equiangular Theorem
GEOMETRY 4.6
TWO COROLLARIES
Equilateral Equiangular Theorem
A Triangle is EQUILATERAL
if and only if
It is EQUIANGULAR

32. Equilateral Equiangular Theorem
GEOMETRY 4.6
TWO COROLLARIES
Equilateral Equiangular Theorem
A Triangle is EQUILATERAL
if and only if
It is EQUIANGULAR
Equilateral Angles are 60 Degrees Theorem
Each angle of an EQUILATERAL Triangle
measures 60 degrees

33. D
GEOMETRY 4.6 A
Given: E C
Prove: B

34. GEOMETRY 4.6

35. GEOMETRY 4.6

36. GEOMETRY 4.6

37. GEOMETRY 4.6

38. GEOMETRY 4.6

39. GEOMETRY 4.6

40. GEOMETRY 4.6

41. GEOMETRY 4.6

42. GEOMETRY 4.6

43. GEOMETRY 4.6 E D C 4
Prove: 3 2 1 A B

44. GEOMETRY 4.6 W Y Z X V
PROVE:

45. GEOMETRY 4.6