1. Objectives
Apply SSS and SAS to construct triangles and solve problems.
Prove triangles congruent by using SSS and SAS.

2. Vocabulary
triangle rigidity
included angle

3. You only need to know that two triangles have three pairs of congruent corresponding sides to say that the triangles are congruent. This can be expressed as the following postulate.

4. Adjacent triangles share a side, so you can apply the Reflexive Property to get a pair of congruent parts.
Remember!

5. Example 1A: Using SSS to Prove Triangle Congruence
Use SSS to explain why ∆ABC  ∆DBC.

6. Check It Out! Example 1B
Use SSS to explain why
∆ABC  ∆CDA.

7. An ______________is an angle formed by two adjacent sides of a polygon.
__ is the included angle between sides AB and BC.

8. 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.

10. The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides.
Caution

11. Example 2A: Engineering Application
The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ  ∆VWZ.

12. Use SAS to explain why ∆ABC  ∆DBC.
Check It Out! Example 2B
Use SAS to explain why ∆ABC  ∆DBC.

13. The SAS Postulate guarantees that if you are given the lengths of two sides and the measure of the included angles, you can construct one and only one triangle.

14. Example 3A: Verifying Triangle Congruence
Show that the triangles are congruent for the given value of the variable.
∆MNO  ∆PQR, when x = 5.

15. Example 3B: Verifying Triangle Congruence
Show that the triangles are congruent for the given value of the variable.
∆STU  ∆VWX, when y = 4.

16. Example 4A: Proving Triangles Congruent
Given: BC ║ AD, BC  AD
Prove: ∆ABD  ∆CDB
Statements
Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5.

17. Given: QP bisects RQS. QR  QS
Check It Out! Example 4B
Given: QP bisects RQS. QR  QS
Prove: ∆RQP  ∆SQP
Statements
Reasons 1. 1. 2 2. 3. 3. 4. 4. 5. 5.