1. CONFIDENTIAL 1 Geometry Triangle Congruence SSS and SAS

2. CONFIDENTIAL 2 Warm Up

3. CONFIDENTIAL 3 Triangle Congruence In the previous lesson, we proved triangles congruent by showing that all six pairs of corresponding parts were congruent. The property of triangle rigidity gives you a shortcut for proving two triangles congruent. It states that if the side lengths of a triangle are given, the triangle can have only one shape. For example, you need to know two triangles have three pairs of congruent corresponding sides. This can be expressed as by some postulates.

4. CONFIDENTIAL 4 Side-Side-Side (SSS) Congruence Hypothesis Conclusion ∆ABC = ∆DEF Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

5. CONFIDENTIAL 5 Using SSS to prove triangle Congruent

6. CONFIDENTIAL 6 Now you try!

7. CONFIDENTIAL 7 An included angle is an angle formed by two adjacent sides of a polygon. /B is the included angle between sides AB and BC. It can also be shown that only two pairs of congruent corresponding sides are needed to prove the congruence of two triangles if the included angles are also congruent. A BC

8. CONFIDENTIAL 8 Side-Angle-Side (SAS) Congruence Hypothesis Conclusion ∆ABC = ∆DEF Postulate: If two sides and included angle of one triangle are congruent to two sides and included angle of another triangle, then the triangles are congruent.

9. CONFIDENTIAL 9

10. 10 Now you try!

11. CONFIDENTIAL 11 The SAS postulate guarantees that if you are given the lengths of two sides and the measure of the included angle, you can construct one and only one triangle.

12. CONFIDENTIAL 12 Construction Congruent triangles using SAS STEP1: Use a straightedge to draw two segments and one angle, or copy the given segments and angle. Construct AB congruent to one of the segment. A B Next page 

13. CONFIDENTIAL 13 STEP2: Construct /A congruent to the given angle. A B STEP3: Construct AC congruent to the other segment. Draw CB to complete ∆ABC. A B C

14. CONFIDENTIAL 14 Verifying triangle Congruence Show that the triangles are congruent for the given value of the variable.

15. CONFIDENTIAL 15

16. CONFIDENTIAL 16 Now you try!

17. CONFIDENTIAL 17 Proving triangles Congruent EG F H l m

18. CONFIDENTIAL 18 Now you try!

19. CONFIDENTIAL 19 Now some practice problems for you!

20. CONFIDENTIAL 20 Assessment Use SSS to explain why the triangles in each pair are congruent.

21. CONFIDENTIAL 21 Show that the triangles are congruent for the given value of the variable.

22. CONFIDENTIAL 22

23. CONFIDENTIAL 23 K J G L H

24. CONFIDENTIAL 24 Triangle Congruence In the previous lesson, we proved triangles congruent by showing that all six pairs of corresponding parts were congruent. The property of triangle rigidity gives you a shortcut for proving two triangles congruent. It states that if the side lengths of a triangle are given, the triangle can have only one shape. For example, you need to know two triangles have three pairs of congruent corresponding sides. This can be expressed as by some postulates. Let’s review

25. CONFIDENTIAL 25 Side-Side-Side (SSS) Congruence Hypothesis Conclusion ∆ABC = ∆DEF Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

26. CONFIDENTIAL 26 Using SSS to prove triangle Congruent

27. CONFIDENTIAL 27 An included angle is an angle formed by two adjacent sides of a polygon. /B is the included angle between sides AB and BC. It can also be shown that only two pairs of congruent corresponding sides are needed to prove the congruence of two triangles if the included angles are also congruent. A BC

28. CONFIDENTIAL 28 Side-Angle-Side (SAS) Congruence Hypothesis Conclusion ∆ABC = ∆DEF Postulate: If two sides and included angle of one triangle are congruent to two sides and included angle of another triangle, then the triangles are congruent.

29. CONFIDENTIAL 29

30. CONFIDENTIAL 30 Verifying triangle Congruence Show that the triangles are congruent for the given value of the variable.

31. CONFIDENTIAL 31 Proving triangles Congruent EG F H l m

32. CONFIDENTIAL 32 You did a great job today!