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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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