1. Class Greeting

2. Objective: The students will be able to Prove Congruence – SSS and SAS.

3. Proving Congruence – SSS and SAS
Chapter 4 – Lesson 3
Proving Congruence – SSS and SAS

4. Postulate 4.1 SSS (side-side-side)
If all 3 sides of one triangle are congruent to the corresponding sides of a second triangle then the triangles are congruent

5. G is the midpoint of both
Given:
G is the midpoint of both
FEG HIG
Prove: G
1. Given 1.
Proof:
Reasons
Statements E H
2. Midpoint Theorem 2.
3. SSS
3. FEG HIG
Example 4-1b

6. Write a two-column proof to prove that ABC GBC if
3. SSS
1. Given
2. Reflexive
Proof:
Reasons
Statements 1. 2.
3. ABC GBC
Example 4-1b

7. COORDINATE GEOMETRY Determine whether WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain.
Use the Distance Formula to show that the corresponding sides are congruent.
Example 4-2a

8. = = = = = = = =
Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS.
Example 4-2b

9. Determine whether ABC DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.
Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, ABC DEF by SSS.
Example 4-2c

10. Given sides AB and CB, B is the included angle
Vocabulary
Included angle (between 2 given sides)
The included angle between 2 given sides of a triangle is the angle whose sides are the two given sides
Given sides AB and CB, B is the included angle

11. Postulate 4.2 SAS (side-angle-side)
If 2 sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle then the two triangles are congruent

12. Write a flow proof.
Given:
Prove: QRT STR
Example 4-3a

13. Answer:
Example 4-3b

14. Write a flow proof.
Given:
Prove: ABC ADC
Example 4-3c

15. Proof:
Midpoint Theorem
Example 4-3d

16. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Answer: SAS
Example 4-4a

17. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
The third side is congruent by the Reflexive Property. So the triangles are congruent by SSS.
Answer: SSS
Example 4-4b

18. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. a.
The third side is congruent by the Reflexive Property. So the triangles are congruent by SAS.
Answer: SAS
Example 4-4c

19. b.
Answer: not possible
Example 4-4d

20. Kahoot!

21. Lesson Summary:
Objective: The students will be able to Prove Congruence – SSS and SAS.

22. Preview of the Next Lesson:
Objective: The students will be able to Prove Congruence – ASA, AAS and HL.

23. Stand Up Please