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. CCGPS Analytic Geometry
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

3. 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?

4. 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?

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

6. 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?

7. 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?

8. 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?

9. 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?

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

11. 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

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

13. 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

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

15. Ex 1
DFE
UVW
by ____
SSS

16. 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

17. 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

18. 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

19. 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

20. 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

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

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

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

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

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

26. Ex 1
DEF
NLM
by ____
ASA

27. 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

28. 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

29. 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

30. 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

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.
Ex 6 E A C B D
ΔACB  ΔECD by SAS

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 7 J T L K V U
Not possible