1. Rigid Motions and
Congruence

2. Rigid Motions
A rigid motion is a transformation that changes the position of a geometric figure without changing its shape or size. Examples of rigid motions include the following transformation:
- Translation
- Reflection
- Rotation

3. Congruent triangles have congruent sides and congruent angles.
The parts of congruent triangles that “match” are called corresponding parts.

4. Alt Int Angles are congruent given parallel lines
Overlapping sides are congruent in each triangle by the REFLEXIVE property
Alt Int Angles are congruent given parallel lines
Vertical Angles are congruent

5. Before we start…let’s get a few things straightC X Z Y
INCLUDED ANGLE

6. Side-Side-Side (SSS) Congruence Postulate4 4 5 5 6 6
All Three sides in one triangle are congruent to all three sides in the other triangle

7. Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle

8. Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included

9. Your Only Ways To Prove Triangles Are Congruent
SSS
SAS
ASA
AAS
NO BAD WORDS
Your Only Ways To Prove Triangles Are Congruent

10. Ex 1
DFE
UVW
by ____
SSS

11. Ex 2
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S Y X Z
ΔRST  ΔYZX by SSS

12. Not enough Information to Tell
Ex 3
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S B A C
Not congruent.
Not enough Information to Tell

13. ΔPQS  ΔPRS by SAS Ex 4 P R Q S
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R Q S
ΔPQS  ΔPRS by SAS

14. ΔPQR  ΔSTU by SSS Ex 5 P S U Q R T
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S U Q R T
ΔPQR  ΔSTU by SSS

15. Not enough Information to Tell
Ex 6
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R Q N
Not congruent.
Not enough Information to Tell

16. Before we start…let’s get a few things straightC X Z Y
INCLUDED SIDE

17. Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side

18. Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included

19. Your Only Ways To Prove Triangles Are Congruent
SSS
SAS
ASA
AAS
NO BAD WORDS
Your Only Ways To Prove Triangles Are Congruent

20. Ex 1
DEF
NLM
by ____
ASA

21. Ex 2
What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N

22. Ex 3
What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N

23. Determine 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.
Ex 4 G I H J K
ΔGIH  ΔJIK by AAS

24. 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 D
Ex 5
ΔABC  ΔEDC by ASA

25. 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.
Ex 6 E A C B D
ΔACB  ΔECD by SAS

26. 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.
Ex 7 J T L K V U
Not possible

27. Complete each congruence statement.B A C D F
DEF E
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

28. Complete each congruence statement.D B
ECD

29. Complete each congruence statement.K G H T
GTK
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

30. Corresponding Parts of Congruent Triangles are Congruent
CPCTC
Corresponding Parts of Congruent Triangles are Congruent

31. O because ________. CPCTC Fill in the blanks
If CAT  DOG, then A  ___
because ________.
CPCTC O D G C A T

32. Q CPCTC B CPCTC Fill in the blanks If FJH  QRS, then ___
and F  ___ because _______. Q
CPCTC
If XYZ  ABC, then ___
and Y  ___ because _______. B
CPCTC