Transcript statement reason

definition of a parallelogram
opposite sides of parallelogram are congruent
opposite angles of a parallelogram are congruent
diagonals of a parallelogram bisect each other
alternate interior angles theorem
consecutive interior angles theorem
alternate interior angles theorem converse
consecutive interior angles theorem converse
definition of a rhombus
C
B
<1 <3
<4
<2
Given:
ABCD is a parallelogram
Prove:
AB = CD
AD = CB
1/7
D
A
statement
reason
ABCD is a parallelogram
Draw AC
given
through any two points there exists
exactly one line
C
B
<1 <3
<4
<2
Given:
ABCD is a parallelogram
Prove:
AB = CD
AD = CB
D
A
statement
reason
ABCD is a parallelogram
Draw AC
given
through any two points there exists
exactly one line
definition of a parallelogram
definition of a parallelogram
alternate interior angles theorem
alternate interior angles theorem
reflexive property
ASA
CPCTC
CPCTC
BC // DA
AB // CD
<1 = <2
<3 = <4
AC = AC
∆ABC = ∆CDA
AB = CD
AD = CB
C
B
<1 <3
<4
Given:
ABCD is a parallelogram
Prove:
<B = <D
hint: opp sides of parallelogram are cong
<2
D
A
statement
reason
ABCD is a parallelogram
Draw AC
given
through any two points there
exists exactly one line
2/7
C
B
<1 <3
<4
Given:
ABCD is a parallelogram
Prove:
<B = <D
hint: opp sides of parallel are cong
<2
D
A
statement
reason
ABCD is a parallelogram
Draw AC
given
through any two points there
exists exactly one line
opposite sides of parallelogram are congruent
opposite sides of parallelogram are congruent
reflexive property
SSS
CPCTC
AB = CD
BC = DA
AC = AC
∆ABC = ∆CDA
<B = <D
2/5
B
C
<1
<3
E
<4
<2
A
Given:
ABCD is a parallelogram
Prove:
AE = CE
BE = DE
D
statement
reason
ABCD is a parallelogram
given
3/7
B
C
<1
<3
E
<4
<2
A
Given:
ABCD is a parallelogram
Prove:
AE = CE
BE = DE
D
statement
reason
ABCD is a parallelogram
<1 = <2
<3 = <4
BC = DA
∆BCE = ∆DAE
AE = CE
BE = DE
given
alternate interior angles theorem
alternate interior angles theorem
opposite sides of parallelogram are congruent
ASA
CPCTC
CPCTC
5/5
C
B
Given:
<3
<4
Prove:
<2
BC // DA
BC = DA
ABCD is a parallelogram
<1
D
A
statement
reason
BC // DA
BC = DA
given
given
4/7
C
B
Given:
BC // DA
BC = DA
Prove:
ABCD is a parallelogram
<3
<4
<2
<1
D
A
statement
reason
BC // DA
BC = DA
<1 = <3
AC = AC
∆ABC = ∆CDA
<2 = <4
AB // CD
ABCD is a parallelogram
given
given
alternate interior angles theorem
reflexive property
SAS
CPCTC
alternate interior angles converse
definition of a parallelogram
C
B
Given:
ABCD is a parallelogram
AC  BD
E
Prove:
AB = AD
D
A
Note: figure not drawn to scale
statement
reason
ABCD is a parallelogram
AC  BD
given
given
5/7
C
B
Given:
ABCD is a parallelogram
AC  BD
Prove:
AB = AD
E
D
A
Note: figure not drawn to scale
statement
reason
ABCD is a parallelogram
given
AC  BD
given
BE = DE
diagonals of a parallelogram bisect
<AEB = 90
definition of  lines
<AED = 90
definition of  lines
<AEB = <AED
substitution
AE = AE
reflexive property
∆AEB = ∆AED
SAS
AB = AD
CPCTC
C
B
E
Given:
ABCD is a rhombus
Prove:
<AEB = 90
D
A
Note: figure not drawn to scale
statement
reason
ABCD is a rhombus
given
6/7
C
B
E
Given:
ABCD is a rhombus
Prove:
<AEB = 90
D
A
Note: figure not drawn to scale
statement
reason
ABCD is a rhombus
AB = BC
AE = CE
BE = BE
∆ABE = ∆CBE
<AEB = <CEB
<AEB + <CEB = 180
<AEB + <AEB = 180
2(<AEB) = 180
<AEB = 90
given
definition of a rhombus
diagonals of a rhombus bisect each other
reflexive property
SSS
CPCTC
linear pair postulate
substitution
combine like terms
division property
B
C
Given:
Prove:
A
ABCD is a parallelogram
AC = BD
<A = 90
D
statement
reason
ABCD is a parallelogram
AC = BD
given
given
7/7
B
C
A
Given:
ABCD is a parallelogram
AC = BD
Prove:
<A = 90
D
statement
reason
ABCD is a parallelogram
AC = BD
AD = BC
AB = AB
∆ABD = ∆BAC
<A = <B
BC // DA
<A + <B = 180
<A + <A = 180
2(<A) = 180
<A = 90
given
given
opposite sides of a parallelogram are equal
reflexive property
SSS
CPCTC
definition of a parallelogram
same side interior angles theorem
substitution
combine like terms
division property