2. CPCTC  ’s Naming  ’s Algebra Connection Proofs Altitudes & Medians 100 200 300 400 500 400 300 200 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500

3. CPCTC - 100 A B D EF C If  ABC   DEF, then  C   F.

4. CPCTC - 200 If  ABC   DEF, then  BCA   EFD

5. CPCTC - 300 If  JKL   ABC, name another way to state that the triangles are congruent.  KLJ   BCA  JLK   ACB  LJK   CAB  LKJ   CBA  KJL   BAC

6. CPCTC - 400 C D BA  ACB  DBC

7. CPCTC - 500 What does the acronym CPCTC stand for? Corresponding Parts of Congruent Triangles are Congruent.

8. Congruent Triangles - 100 Which method(s) can you use to prove that the given triangles are congruent? SSS C AB D  ABC   DCB

9. Congruent Triangles - 200 Which method(s) can you use to prove that the given triangles are congruent? A D F K L B  ABD   FKL HL

10. Congruent Triangles - 300 Which method(s) can you use to prove that the given triangles are congruent? L M NP SAS, AAS, ASA  LPN   NML

11. Congruent Triangles - 400 Which method(s) can you use to prove that the given triangles are congruent? B A D C  ABC   DCB SAS

12. Congruent Triangles - 500 Which method(s) can you use to prove that the given triangles are congruent? AC D B DB is a median and an altitude of  ADC.  ABD   CBD SAS

13. Naming Triangles - 100 K L J C B A  ABC  JKL

14. Naming Triangles - 200 H G K J  HJG  KJG

15. Naming Triangles - 300 DC BA  ABD  CDB

16. Naming Triangles - 400  JKL  M J K L  LMJ

17. Naming Triangles - 500  ABC  B A C D E F NONE! There is not sufficient evidence to conclude that the two triangles are congruent!

18. Algebra Connection - 100 x 3x - 14 Solve for x. x = 26

19. Algebra Connection - 200 2x3x 4x x = 20 Solve for x.

20. Algebra Connection - 300 5x + 126x + 2 y Solve for x and y. x = 10y = 56

21. Algebra Connection - 400 Solve for x and y. y x x 30  x = 75y = 105

22. Algebra Connection - 500 Find x. Classify this triangle by its sides and angles. Name the longest and shortest sides. 2x B C A Figure not drawn to scale. 7x - 2 4x x = 14 Sides: Scalene Angles: Obtuse Longest: AB Shortest: AC

23. Proofs 1 - 100 Draw a logical conclusion from the given statement and state the reason. AB D Given: D is the midpoint of AB AD  DB because of the definition of a midpoint.

24. Proofs 1 - 200 Draw a logical conclusion from the given statement and state the reason. A B C D Given: AC is the angle bisector of  BAD. 1.  BAC   CAD because of the definition of an angle bisector.

25. Proofs 1 - 300 Draw a logical conclusion from the given statement and state the reason. BC D A Given: BD is an altitude of  ABC AC  BD because of the definition of an altitude.

26. Proofs 1 - 400 A C D Given: BD bisects  ABC;  ADB   CDB Prove: AB  CB 1. 2. 3. 4. 5. 6. B BD bisects  ABC 1. Given  ABD   CBD Definition of an  bisector  ADB   CDBGiven BD  BDReflexive  ABD   CBDASA AB  CB CPCTC

27. Proofs 1 - 500 Given: AC is a median. AB  AD Prove:  ABC   ADC StatementsReasons A B C D 1. AC is a median.1. Given 2. 3. 4. 5. 6. C is the midpoint of BD. Definition of a median. BC  CDDef. of a midpoint. AB  AD Given AC  AC Reflexive  ABC   ADCSSS

28. Medians and Altitudes - 100 Name a median. A E D C B AD

29. Medians and Altitudes - 200 Name an altitude. A E D C B EB

30. Medians and Altitudes - 300 Identify BC as a median, altitude, perpendicular bisector, angle bisector or none of these. C B None of these.

31. Medians and Altitudes - 400 In which type of triangle do two of the altitudes lie on the outside of the triangle? An Obtuse Triangle.

32. Medians and Altitudes - 500 Identify BC as a median, altitude, perpendicular bisector, angle bisector or none of these. C B Median