Proof of Theorem 4.8 – The Base Angles Theorem Given: WX WY ZW bisects XY Prove: X Y...
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Proof of Theorem 4.8 – The Base Angles Theorem Given: WX WY ZW bisects XY Prove: X Y Statement s Reasons S WX WY Given Z Y X W
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Transcript of Proof of Theorem 4.8 – The Base Angles Theorem Given: WX WY ZW bisects XY Prove: X Y...
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
XZ ZY
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
XZ ZY Definition of Segment Bisector
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
S XZ ZY Definition of Segment Bisector
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
S XZ ZY Definition of Segment Bisector
WZ WZ
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
S XZ ZY Definition of Segment Bisector
S WZ WZ Reflexive P of C
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
S XZ ZY Definition of Segment Bisector
S WZ WZ Reflexive P of C
WXZ YXZZ YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
S WX WY Given
ZW Bisects XY
Given
S XZ ZY Definition of Segment Bisector
S WZ WZ Reflexive P of C
WXZ YXZ
SSSZ YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
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
Z YX
W
Proof of Theorem 4.8 – The Base Angles TheoremGiven: WX WY
ZW bisects XYProve: X Y
Statements Reasons
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
Z YX
W
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
ABD, CDB are right angles
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
ABD, CDB are right angles
Definition of Perpendicular Lines
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
ABD, CDB are right angles
Definition of Perpendicular Lines
BDA, BDC are right ’s
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
ABD, CDB are right angles
Definition of Perpendicular Lines
BDA, BDC are right ’s
Definition of Right Triangle
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
BD AC Given
ABD, CDB are right angles
Definition of Perpendicular Lines
BDA, BDC are right ’s
Definition of Right Triangle
BC AB
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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 BDD C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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 CD C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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 CD C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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 CD C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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 HLD C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
Given: BD ACBC AB
Prove: BD Bisects ABC
Statements Reasons
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
D C
B
A
