Transcript Is it As Parallelogram?

Is it As Parallelogram?
Is it As Parallelogram?
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This figure has no parallel lines or
congruent sides.
One pair of opposite angles are congruent
but the other is not.
It is NOT a Parallelogram
This figure is a Parallelogram
Reason: Both pair of opposite angles
are congruent
Because of Alternate Interior Angles
Converse, the top and bottom sides are
parallel.
Since none of the arcs touch the left or right
Sides, we do not have enough information to
Say the left and right sides are parallel.
This figure is NOT a Parallelogram
110
70
110
This figure has one angle (70) that is
Supplementary to its two
consecutive angles (110).
This figure is a parallelogram.
Reason: One angle is supplementary
to its two consecutive angles.
This figure is a parallelogram.
Reason: Diagonals bisect each other.
The single arcs make the top and bottom
parallel. The double arcs make the left and
right parallel. Both of these are by the
Alternate Interior Angles Converse(2x).
This figure is a parallelogram.
Reason: Definition of parallelogram
(Both pair of opposite sides are parallel.)
The single arcs make the top and bottom
parallel. The double arcs make the left and
right parallel. Both of these are by the
Alternate Interior Angles Converse(2x).
This figure is a parallelogram.
Reason: Definition of parallelogram
(Both pair of opposite sides are parallel.)
The hash marks mean the top and bottom
are congruent. The arcs make the top and
bottom parallel by
Corresponding Angles Converse.
This figure is a parallelogram.
Reason: One Pair of opposite sides is
both parallel and congruent.
The hash marks mean the left and right are
congruent. The arrowheads mean that the
top and bottom are parallel.
This figure is NOT a parallelogram.
Since these are not the same pair
of sides, It is not a parallelogram.
The hash marks mean the three segments
are congruent. This is not enough information
to say that it is a parallelogram.
This figure is NOT a parallelogram.
The arcs are marking vertical angle pairs.
This does not make any sides congruent or
any sides parallel. It is insufficient information
for a parallelogram.
This figure is NOT a parallelogram.
5 cm
5 cm
The left and right sides are the same length
and they are also parallel.
This figure IS a parallelogram.
Reason: One Pair of sides is both
parallel and congruent.
The top and bottom are parallel because
of the Alternate Interior Angles Converse.
The left and right sides are parallel because
of the Corresponding Angles Converse.
This figure IS a parallelogram.
Reason: Definition of Parallelogram.
This figure IS NOT a parallelogram.
The opposite sides are not the same lengths.
Since all right angles are congruent,
the opposite angles are congruent.
Other reasons also apply.
This figure IS a parallelogram.
Reason: Both Pair of opposite angles
are congruent.
Left and right sides are parallel and
top and bottom are parallel.
This figure IS a parallelogram.
Reason: Definition of Parallelogram.
Left and right sides are congruent and top
and bottom are congruent.
This figure IS a parallelogram.
Reason: Both pair of opposite sides are
congruent.
Even though the top and bottom are
congruent and one pair of opposite angles
are congruent, this is insufficient to ensure
a parallelogram.
This figure IS NOT a parallelogram.
The diagonals are NOT bisecting each other .
This figure IS NOT a parallelogram.
Even though the arcs mean that the top and
bottom segments are parallel by the
Alternate Exterior Angles Converse, that is all
we know. We don’t know the other pair is
parallel and we don’t know if the top and
bottom are congruent.
This figure IS NOT a parallelogram.
By Reflexive and AAS, these two triangles are
congruent, so their corresponding sides will
be congruent by CPCTC. This means the left
and right sides are congruent and the top
and bottom are congruent. (other reasons
work too)
This figure IS a parallelogram.
Reason: Both Pair of opposite sides
are congruent.
By Consecutive Interior Angles Converse, we
know that the top and bottom will be parallel.
However, this is not enough to make it a
parallelogram.
This figure IS NOT a parallelogram.
A
Quad ABCD
AB  BC
CD  AD
AB  BC
B
Aa
D
C
There is no reason that includes adjacent
sides being congruent.
This figure IS NOT a parallelogram.
Quad ABCD A
ABBC
ABAD
AD  BC
AB AD
BC
B
Aa
D
C
Since BC and AD are perpendicular to the
same segment, AB, then they are parallel by
two lines perpendicular to the
same line are parallel.
This figure IS a parallelogram.
Reason: One Pair of opposite sides
are both parallel and congruent.
AB AD
AE
BC
EC
Quad ABCD
Diagonals
intersect at E
AEEC
BE  ED
D
A
Aa
B
E
C
Since the two diagonals are bisecting each
other, it is a parallelogram.
This figure IS a parallelogram.
Reason: Diagonals bisect each other.
A
Quad ABCD
AC  BD
AB  BC
B
Aa
D
C
There is no reason that includes that the
diagonals are congruent to each other.
This figure IS NOT a parallelogram.
AB AD
BC
A
Quad ABCD
AC  BD
AC  BD
B
Aa
D
C
Even though the diagonals are congruent
and perpendicular, this is not a reason used
to verify a parallelogram.
This figure IS NOT a parallelogram.
A
Quad ABCD
A  B
C  D
AB  BC
B
Aa
D
C
Parallelograms have two pair of opposite
angles congruent, not two pair of adjacent
angles.
This figure IS NOT a parallelogram.
Quad ABCD
A & B are
supplementary
C & D are
supplementary
AB A
 BC
B
Aa
D
C
The Consecutive Interior Angles Converse
makes segments
AD and BC parallel. However, just two
parallel segments do not make a
parallelogram. .
This figure IS NOT a parallelogram.
A
Quad ABCD
A  C
D  B
AB  BC
B
Aa
D
C
This figure IS a parallelogram.
Reason: Both Pair of opposite
angles are congruent.
Quad ABCD
A & D are
supplementary
C & D are
supplementary
AB A
 BC
B
Aa
D
C
Since angle D is supplementary to its two
consecutive angles, A and C, it is enough to
say it is a parallelogram.
This figure IS a parallelogram.
Reason: One angle is supplementary
to both its consecutive angles.
Quad ABCD
mA = 15
mB = 115
mC = 15
A
15
15
D
115
B
15
C
Since 115 + 15  180, the consecutive angles
are not supplementary, so it is not a
parallelogram.
This figure IS NOT a parallelogram.