2. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Warm Up 9/29/08 1.Give the restrictions on the third side of the triangle if the first two sides are 18 and 30. 2. Find x and y for both figures. 55°70°x y 100°2x + 10 4y 80

3. Math I Day 35 (9-29-08) UNIT QUESTION: What are the properties and characteristics of polygons? Standard: MM1G1.e. Today’s Question: What does it mean for two triangles to be congruent? Standard: MM1G.3.c.

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

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

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

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

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

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

10. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Fill in the blanks If  FJH   QRS, then ___ and  F  ___ because _______. QQ CPCTC BB If  XYZ   ABC, then ___ and  Y  ___ because _______.

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

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

13. Before we start…let’s get a few things straight AB C XZ Y INCLUDED ANGLE

14. Side-Side-Side (SSS) Congruence Postulate 66 4 4 5 5 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 DFEUVW by ____ SSS

17. 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 Ex 2

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

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

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

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

22. Before we start…let’s get a few things straight INCLUDED SIDE AB C XZ Y

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. Your Only Ways To Prove Triangles Are Congruent NO BAD WORDS

26. Ex 1 DEFNLM 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 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. ΔGIH  ΔJIK by AAS G I H J K Ex 4

30. ΔABC  ΔEDC by ASA BA C ED Ex 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.

31. ΔACB  ΔECD by SAS B A C E D Ex 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.

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

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