1. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts.

2. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

3. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

4. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

5. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

6. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

7. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

8. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC D EF Below we have ∆ABC and ∆DEF. They look similar, like you could fit one exactly on top of the other. They contain corresponding parts.

9. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F These two triangles look similar but are not “ lined up”. If we can prove they have certain corresponding parts that are congruent, we can prove they are congruent triangles.

10. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Side Angle Side Postulate ( SAS ) – two triangles are congruent if two sides of one triangle and the angle between them are congruent to the corresponding parts of the second triangle.

11. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Side Angle Side Postulate ( SAS ) – two triangles are congruent if two sides of one triangle and the angle between them are congruent to the corresponding parts of the second triangle.

12. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Side Angle Side Postulate ( SAS ) – two triangles are congruent if two sides of one triangle and the angle between them are congruent to the corresponding parts of the second triangle.

13. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Side Angle Side Postulate ( SAS ) – two triangles are congruent if two sides of one triangle and the angle between them are congruent to the corresponding parts of the second triangle. We have enough given information to use SAS to prove these triangles congruent.

14. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Side Angle Postulate ( ASA ) – two triangles are congruent if two angles of one triangle and the side between them are congruent to the corresponding parts of the second triangle.

15. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Side Angle Postulate ( ASA ) – two triangles are congruent if two angles of one triangle and the side between them are congruent to the corresponding parts of the second triangle.

16. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Side Angle Postulate ( ASA ) – two triangles are congruent if two angles of one triangle and the side between them are congruent to the corresponding parts of the second triangle.

17. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Side Angle Postulate ( ASA ) – two triangles are congruent if two angles of one triangle and the side between them are congruent to the corresponding parts of the second triangle. We have enough given information to use ASA to prove these triangles congruent.

18. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent.

19. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :Sometimes the information needed is “given” at the beginning of the problem.

20. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :Sometimes the information needed is “given” at the beginning of the problem. Using that information, mark your triangles corresponding parts…

21. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :Sometimes the information needed is “given” at the beginning of the problem. Using that information, mark your triangles corresponding parts…

22. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :Sometimes the information needed is “given” at the beginning of the problem. Using that information, mark your triangles corresponding parts…

23. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :Sometimes the information needed is “given” at the beginning of the problem. Using that information, mark your triangles corresponding parts…

24. Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts. A BC DE F Angle Angle Side Theorem ( AAS ) – if two angles and a non included side of one triangle are congruent to the corresponding angles and non included side of another triangle, then the triangles are congruent. Given :We have enough given information to use AAS to prove these triangles congruent.

25. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 1 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F

26. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 1 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see :

27. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 1 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see : We need another side where the angle is formed by the sides :

28. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 1 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see : We need another side where the angle is formed by the sides :

29. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 2 : What missing information would you need to prove these triangles congruent using the ASA Postulate ? A B C D E F

30. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 2 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see :

31. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 2 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see : We need another angle where the side is between them :

32. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 2 : What missing information would you need to prove these triangles congruent using the SAS Postulate ? A B C D E F From the diagram we can see : We need another angle where the side is between them :

33. Triangles and Lines – Congruent Triangles Side Side Side Postulate ( SSS ) – Two triangles are congruent if all three sides of one triangle are congruent to all three sides of another triangle.

34. Triangles and Lines – Congruent Triangles. A B C D E F Side Side Side Postulate ( SSS ) – Two triangles are congruent if all three sides of one triangle are congruent to all three sides of another triangle.

35. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 3 : What missing information would you need to prove triangle ABD and triangle BCD congruent using the SSS Postulate ? A B C D

36. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 3 : What missing information would you need to prove triangle ABD and triangle BCD congruent using the SSS Postulate ? A B C D From the diagram we see :

37. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 3 : What missing information would you need to prove triangle ABD and triangle BCD congruent using the SSS Postulate ? A B C D From the diagram we see : These triangles also share a side so :

38. Triangles and Lines – Congruent Triangles Let’s look at how to use these postulates and theorems. Example # 3 : What missing information would you need to prove triangle ABD and triangle BCD congruent using the SSS Postulate ? A B C D From the diagram we see : These triangles also share a side so : Our missing information is :