Transcript Statement Reason

reflexive property
B
Given:
A
<1
<3
<2
<4
Prove:
AB = AD
BC = DC
∆ABC = ∆ADC
C
D
Statement
Reason
AB = AD
BC = DC
given
given
B
Given:
A
<1
<3
<2
<4
Prove:
AB = AD
BC = DC
∆ABC = ∆ADC
C
D
Statement
Reason
AB = AD
BC = DC
AC = AC
∆ABC = ∆ADC
given
given
reflexive property
SSS
B
A
<1
<3
<2
<4
C
Given:
AC bisects <A
AC bisects <C
Prove:
∆ABC = ∆ADC
D
Statement
Reason
AC bisects <A
AC bisects <C
given
given
B
A
<1
<3
<2
<4
C
Given:
AC bisects <A
AC bisects <C
Prove:
∆ABC = ∆ADC
D
Statement
Reason
AC bisects <A
AC bisects <C
<1 = <2
<3 = <4
AC = AC
∆ABC = ∆ADC
given
given
definition of an angle bisector
definition of an angle bisector
reflexive property
ASA
B
A
<1
<3
<2
<4
C
Given:
AB = AD
AC bisects <A
Prove:
∆ABC = ∆ADC
D
Statement
Reason
AB = AD
AC bisects <A
given
given
B
A
<1
<3
<2
<4
C
Given:
AB = AD
AC bisects <A
Prove:
∆ABC = ∆ADC
D
Statement
Reason
AB = AD
AC bisects <A
<1 = <2
AC = AC
∆ABC = ∆ADC
given
given
definition of an angle bisector
reflexive property
SAS
B
Given:
D is the midpoint of AC
AB = CB
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
D is the midpoint of AC
AB = CB
given
given
B
Given:
D is the midpoint of AC
AB = CB
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
D is the midpoint of AC
AB = CB
AD = CD
BD = BD
∆ABD = ∆CBD
given
given
definition of a midpoint
reflexive property
SSS
B
Given:
BD bisects <ABC
AB = CB
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
BD bisects <ABC
AB = CB
given
given
B
Given:
BD bisects <ABC
AB = CB
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
BD bisects <ABC
AB = CB
<1 = <2
BD = BD
∆ABD = ∆CBD
given
given
definition of an angle bisector
reflexive property
SAS
B
Given:
<4 = 90°
D is the midpoint of AC
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
<4 = 90°
D is the midpoint of AC
given
given
B
Given:
<4 = 90°
D is the midpoint of AC
Prove:
∆ABD = ∆CBD
<1 <2
A
<3 <4
D
C
Statement
Reason
<4 = 90°
D is the midpoint of AC
<3 + <4 = 180
<3 + 90 = 180
<3 = 90
<3 = <4
AD = CD
BD = BD
∆ABD = ∆CBD
given
given
linear pair postulate
substitution
subtraction
substitution
definition of a midpoint
reflexive property
SAS