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Is it As Parallelogram? Is it As Parallelogram? Row 1 Row 5 Row 9 Row 6 Row 10 Row 2 Row 3 Row 7 Row 4 Row 8 Row 11 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 ABBC ABAD 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 AEEC 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 mA = 15 mB = 115 mC = 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.