1. 4.4 - Prove Triangles Congruent by SAS and HL

2. Included Angle: Angle in-between two congruent sides

3. 1. Use the diagram to name the included angle between the given pair of sides. HH

4.  HIG

5. 1. Use the diagram to name the included angle between the given pair of sides.  JGI

6. Side-Angle-Side (SAS) Congruence Postulate A BCD4cm EF

7. If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________ included congruent

8. Right Triangles: leg hypotenuse

9. Hypotenuse-Leg (HL) Congruence Theorem: If the _______________ and a ________ of a ___________ triangle are ____________ to the _____________ and ________ of a second _________ triangle, then the two triangles are _________________. hypotenuse leg rightcongruent hypotenuseleg right congruent

11. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS

12. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS

13. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS

14. 2. Decide whether the triangles are congruent. Explain your reasoning. No, AD ≠ CD

15. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS

16. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, HL

17. 2. Decide whether the triangles are congruent. Explain your reasoning. No, Not a right triangle

18. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SSS

19. 2. Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS

20. 3. State the third congruence that must be given to prove  ABC   DEF. GIVEN:  B   E,, ______  ______. Use the SAS Congruence Postulate.

21. 3. State the third congruence that must be given to prove  ABC   DEF. GIVEN:, ______  ______. Use the SSS Congruence Postulate.

22. 3. State the third congruence that must be given to prove  ABC   DEF. GIVEN:  A is a right angle and  A   D. Use the HL Congruence Theorem.

23. 4. Given: Prove: ∆RGI  ∆TGH 1. given 2. Def. of midpt 3. Def. of midpt 4. 5. Vertical angles  RGI   TGH ∆RGI  ∆TGH SAS

24. 5. Given: Prove: ∆ABD  ∆CDB StatementsReasons Given D A B C 1.

25. D A B C

26. Given  CDB   ABD Alternate Interior Angles Given ∆ABD  ∆CDB SAS Reflexive D A B C 1. 2. 3. 4. 5. Statements Reasons 5. Given: Prove: ∆ABD  ∆CDB

27. 6. Given: Prove: ∆ACD  ∆ACB A BCD Given Def. of Angle Bisector Given ∆ACD  ∆ACB SAS Reflexive 1. 2. 3. 4. 5. Statements Reasons

28. 7. Given: Prove: ∆ACD  ∆ACB A BCD Given Def. of perp. lines Reflexive All right angles are  1. 2. 3. 4. 5. Statements Reasons ∆ACD  ∆ACB HL6.  ACD and  ACB are right angles

29. Ans: HW Problem SectionPage #Assignment Spiral ?s 4.42433-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all) 9-11 # 27

30. HW Problem SectionPage #Assignment Spiral ?s 4.42433-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all) 9-11 # 26