Warm Up On Desk (5 min) Do Daily Quiz 5.1 (10 min)

1. Warm Up On Desk (5 min)Do Daily Quiz 5.1 (10 min)

2. Review -go over the Daily Quiz items in 5.1

3. 5.2 ESSENTIAL OBJECTIVE • Show triangles are congruent using SSS and SAS.

4. In Exercises 1–5, use the triangles below. Determine whether the given angles or sides represent corresponding angles, corresponding sides,or neither. 1. B andH Corresponding angles ANSWER DB and HK 2. neither ANSWER

5. Complete the statement with the corresponding congruent part. D ANSWER ? J  _____ 3. ? KH 4. ANSWER CB  _____ 5. The triangles are congruent. Identify all pairs of corresponding congruent parts. Then write a congruence statement. B  H, D  J, C  K,BD  HJ, BC  HK, CD KJ;∆BCD  ∆HKJ ANSWER

6. 5.2

7. VOCABULARY • A proof is a convincing argument that shows why a statement is true.

8. Side-Side-Side Congruence Postulate (SSS) • If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

9. Does the diagram give enough information to show that the triangles are congruent? Explain. Example 1 Use the SSS Congruence Postulate SOLUTION From the diagram you know that HJ LJ and HK  LK. By the Reflexive Property, you know that JK JK. Yes, enough information is given. Because corresponding sides are congruent, you can use the SSS Congruence Postulate to conclude that ∆HJK  ∆LJK. ANSWER

10. Side-Angle-Side Congruence Postulate (SAS) • If two 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.

13. a. Example 2 Use the SAS Congruence Postulate Does the diagram give enough information to use the SAS Congruence Postulate? Explain your reasoning. SOLUTION From the diagram you know that AB CB and DB DB. a. angle ABD and angle CBD are (coz both are 90) Yes, we can use the SAS Congruence Postulate to conclude that ∆ABD ∆CBD.

14. Example 2 Use the SAS Congruence Postulate b. You know that GF GH and GE GE. However, it does not follow the SAS congruence postulate. So, No, we cannot use the SAS Congruence Postulate.

15. Introducing: Two Column Proof

17. SOLUTION To set up the two column proof, start with the given: Example 3 Write a Proof Write a two-column proof that shows ∆JKL  ∆NML. JL  NL Lis the midpoint of KM. ∆JKL  ∆NML

18. Example 3 Write a Proof Statements Reasons JL  NL 1. 1. Given (Side) (Side) 2. 2. Lis the midpoint of KM. Given 3. Definition of midpoint 3. KL  ML 4. JLK  NLM 4. Vertical Angles Theorem (An included angle!)

19. Example 3 Write a Proof Statements Reasons JL  NL 1. 1. Given Side side 2. 2. Lis the midpoint of KM. Given 5. SAS Congruence Postulate 5. ∆JKL  ∆NML 3. Definition of midpoint 3. KL  ML 4. JKL  NML 4. Vertical Angles Theorem An included angle

20. From the figure,  and  . Write a proof to show that ∆DRA∆DRG. D A G R SOLUTION 1. Make a diagram and label it with the given information. Example 4 DR AG RA RG

21. Checkpoint AC  Statements Reasons _____ _____ _____ _____ ? ? ? ? CE CB  1. 1. 2. 2. Given DC 3. BCA  ECD 3. 4. ∆BCA  ∆ECD 4. Prove Triangles are Congruent Example. , ∆BCA  ∆ECD CB  CE ANSWER ANSWER ANSWER ANSWER

22. Statements Reasons 4. Right angles are congruent. 5. Reflexive Property of Congruence 6. SAS Congruence Postulate Example 4 Prove Triangles are Congruent 4. DRA  DRG side 5. DR  DR 6. ∆DRA  ∆DRG angle RA  RG Given 1. 1. side DRAG 2. 2. Given  3. DRAand DRG are right angles. 3. lines form right angles. 

23. Checkpoint AC  AC  Statements Reasons _____ _____ _____ _____ ? ? ? ? DC CE CB  1. 1. Given ANSWER 2. 2. Given ANSWER DC Vertical Angles Theorem 3. BCA  ECD 3. ANSWER SAS Congruence Postulate 4. ∆BCA  ∆ECD 4. ANSWER Prove Triangles are Congruent Fill in. , ∆BCA  ∆ECD CB  CE

24. Hw 5.2A