1. and are midsegments of the triangle.
Session Daily Check
and are midsegments of the triangle.
Find the length of RT and UW. (2 points each)
2) Use the Triangle Proportionality Theorem to solve for x.
(3 points each)
a) b)

2. Homework Review
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

3. CCGPS Analytic Geometry Day 6
UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms?
Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13
Today’s Question:
What does it mean for two triangles to be congruent?
Standard: MCC9-12.G.SRT5, CO.7-8

4. 5-4 Congruent Triangles
Congruent triangles have congruent sides and congruent angles.
The parts of congruent triangles that “match” are called corresponding parts.
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

5. 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?

6. Complete each congruence statement.D B
ECD
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

7. 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?

8. Corresponding Parts of Congruent Triangles are Congruent
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

9. O because ________. CPCTC Fill in the blanks
If CAT  DOG, then A  ___
because ________. O
CPCTC O D G C A T
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

10. 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
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

11. Congruence of Triangles
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

12. 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

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

14. 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

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

16. Ex 1
DFE
UVW
by ____
SSS

17. 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

18. 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

19. 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

20. 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

21. 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

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

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

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

25. There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES… Hypotenuse Leg HL

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

27. Ex 1
DEF
NLM
by ____
ASA

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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