Bunuel wrote:
Is quadrilateral PQRS a parallelogram?
(1) Adjacent sides PQ and QR have the same length.
(2) Adjacent sides RS and SP have the same length.
DS51602.01
OG2020 NEW QUESTION
Statement One Alone:
Adjacent sides PQ and QR have the same length.
Quadrilateral PQRS might or might not be a parallelogram. For example, if RS and SP also have the same length as PQ and QR (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if RS and SP don’t have the same length as PQ and QR (for example, PQ = QR = 4 and RS = SP = 5), then it’s not a parallelogram. Statement one alone is not sufficient.
Statement Two Alone:
Adjacent sides RS and SP have the same length.
Quadrilateral PQRS might or might not be a parallelogram. For example, if PQ and QR also have the same length as RS and SP (for example, RS = SP = PQ = QR = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if PQ and QR don’t have the same length as RS and SP (for example, RS = SP = 4 and PQ = QR = 5), then it’s not a parallelogram. Statement two alone is not sufficient.
Statements One and Two Together:
Even with two statements, quadrilateral PQRS might or might not be a parallelogram. If all 4 sides have the same length (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). However, if PQ = QR = 4 and RS = SP = 5, then it’s not a parallelogram.
Answer: E
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