1. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given

2. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given

3. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given

4. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given XZ  ZY

5. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given XZ  ZY Definition of Segment Bisector

6. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector

7. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector WZ  WZ

8. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector S WZ  WZ Reflexive P of C

9. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector S WZ  WZ Reflexive P of C  WXZ   YXZ

10. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector S WZ  WZ Reflexive P of C  WXZ   YXZ SSS

11. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector S WZ  WZ Reflexive P of C  WXZ   YXZ SSS  X   Y

12. Proof of Theorem 4.8 – The Base Angles Theorem Given: WX  WY ZW bisects XY Prove:  X   Y StatementsReasons S WX  WY Given ZW Bisects XY Given S XZ  ZY Definition of Segment Bisector S WZ  WZ Reflexive P of C  WXZ   YXZ SSS  X   Y CPCTC

13. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given

14. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles

15. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines

16. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s

17. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle

18. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle BC  AB

19. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given

20. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given BD  BD

21. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given BD  BD Reflexive P of C

22. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C

23. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C

24. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC

25. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC HL

26. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC HL  ABD   CBD

27. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC HL  ABD   CBD CPCTC

28. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC HL  ABD   CBD CPCTC BD Bisects  ABC

29. Given: BD  AC BC  AB Prove: BD Bisects  ABC StatementsReasons BD  AC Given  ABD,  CDB are right angles Definition of Perpendicular Lines  BDA,  BDC are right  ’s Definition of Right Triangle S BC  AB Given S BD  BD Reflexive P of C  BDA   BDC HL  ABD   CBD CPCTC BD Bisects  ABC Def of Angle Bisector