Transcript Statement Reason

CPCTC
B
C
Given:
E is the midpoint of BD
<B = <D
Prove:
AB = CD
E
<1
A
<2
D
Statement
Reason
E is the midpoint of BD
<B = <D
given
given
B
C
Given:
E is the midpoint of BD
<B = <D
Prove:
AB = CD
E
<1
A
<2
D
Statement
Reason
E is the midpoint of BD
<B = <D
BE = DE
<1 = <2
∆ABC = ∆CDE
AB = CD
given
given
definition of a midpoint
vertical angle theorem
ASA
CPCTC
B
C
Given:
E is the midpoint of BD
<A = <C
Prove:
<B = <D
E
<1
A
<2
D
Statement
Reason
E is the midpoint of BD
<A = <C
given
given
B
C
Given:
E is the midpoint of BD
<A = <C
Prove:
<B = <D
E
<1
A
<2
D
Statement
Reason
E is the midpoint of BD
<A = <C
BE = DE
<1 = <2
∆ABC = ∆CDE
<B = <D
given
given
definition of a midpoint
vertical angle theorem
AAS
CPCTC
B
C
E
<2
<3
<1
Given:
AB // DC
AB = DC
Prove:
BE = DE
(using ASA)
<5
<4
<6
A
D
Statement
Reason
AB // DC
AB = DC
given
given
B
C
E
<2
<3
<1
A
Given:
AB // DC
AB = DC
Prove:
BE = DE
(using ASA)
<5
<4
<6
D
Statement
Reason
AB // DC
AB = DC
<2 = <6
<1 = <5
∆ABC = ∆CDE
BE = DE
given
given
alternate interior angle theorem
alternate interior angle theorem
ASA
CPCTC
B
C
E
<2
<3
<1
Given:
AB // DC
AB = DC
Prove:
AE = CE
(using AAS)
<5
<4
<6
A
D
Statement
Reason
AB // DC
AB = DC
given
given
B
C
E
<2
<3
<1
A
Given:
AB // DC
AB = DC
Prove:
AE = CE
(using AAS)
<5
<4
<6
D
Statement
Reason
AB // DC
AB = DC
BE = DE
<1 = <5
<3 = <4
∆ABC = ∆CDE
AE = CE
given
given
definition of a midpoint
alternate interior angle theorem
vertical angle theorem
AAS
CPCTC
B
Given:
A
<1
<3
<2
<4
Prove:
AB = AD
BC = DC
<1 = <2
C
D
Statement
Reason
AB = AD
BC = DC
given
given
B
Given:
A
<1
<3
<2
<4
Prove:
AB = AD
BC = DC
<1 = <2
C
D
Statement
Reason
AB = AD
BC = DC
AC = AC
∆ABC = ∆ADC
<1 = <2
given
given
reflexive property
SSS
CPCTC
B
A
<1
<3
<2
<4
C
Given:
AC bisects <A
AC bisects <C
Prove:
<B = <D
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:
<B = <D
D
Statement
Reason
AC bisects <A
AC bisects <C
<1 = <2
<3 = <4
AC = AC
∆ABC = ∆ADC
<B = <D
given
given
definition of an angle bisector
definition of an angle bisector
reflexive property
ASA
CPCTC
B
Given:
D is the midpoint of AC
AB = CB
Prove:
<1 = <2
<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:
<1 = <2
<1 <2
A
<3 <4
D
C
Statement
Reason
D is the midpoint of AC
AB = CB
AD = CD
BD = BD
∆ABD = ∆CBD
<1 = <2
given
given
definition of a midpoint
reflexive property
SSS
CPCTC
B
Given:
<4 = 90°
D is the midpoint of AC
Prove:
<A = <C
<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:
<A = <C
<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
<A = <C
given
given
linear pair postulate
substitution
subtraction
substitution
definition of a midpoint
reflexive property
SAS
CPCTC
B
A
<1
<3
<2
<4
C
Given:
AC bisects <A
AC bisects <C
Prove:
<B = <D
(w/o using ∆ congruence)
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:
<B = <D
(w/o using ∆ congruence)
D
Statement
Reason
AC bisects <A
AC bisects <C
<1 = <2
<3 = <4
<1 + <3 + <B= 180
<2 + <4 + <D = 180
<1 + <3 + <B = <2 + <4 + <D
<2 + <4 + <B = <2 + <4 + <D
<B = <D
given
given
definition of angle bisector
definition of angle bisector
triangle sum theorem
triangle sum theorem
substitution
substitution
subtraction property