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a) Which of the following would be enough information to prove that quadrilateral QRST is a parallelogram? e QR = ST I b) OR IST c) QP = PS and TP = PR d) Two pairs of sides are congruent.

a) Which of the following would be enough information to prove that quadrilateral QRST is a parallelogram? e QR = ST I b) OR IST c) QP = PS and TP = PR d) Two pairs of sides are congruent.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Question:** Which of the following would be enough information to prove that quadrilateral \(QRST\) is a parallelogram? **Diagram Description:** The diagram shows quadrilateral \(QRST\) with diagonals \(QT\) and \(RS\) intersecting at point \(P\). **Answer Choices:** a) \( \overline{QR} \equiv \overline{ST} \) b) \( \overline{QR} \parallel \overline{ST} \) c) \( \overline{QP} \equiv \overline{PS} \) and \( \overline{TP} \equiv \overline{PR} \) d) Two pairs of sides are congruent. **Explanation:** To determine if a quadrilateral is a parallelogram, we should confirm any of the following conditions: 1. Opposite sides are parallel. 2. Opposite sides are congruent. 3. Diagonals bisect each other. 4. One pair of opposite sides is both parallel and congruent. In this problem, the best choice would be based on the given criteria that can verify the presence of these conditions.
Transcribed Image Text:**Question:** Which of the following would be enough information to prove that quadrilateral \(QRST\) is a parallelogram? **Diagram Description:** The diagram shows quadrilateral \(QRST\) with diagonals \(QT\) and \(RS\) intersecting at point \(P\). **Answer Choices:** a) \( \overline{QR} \equiv \overline{ST} \) b) \( \overline{QR} \parallel \overline{ST} \) c) \( \overline{QP} \equiv \overline{PS} \) and \( \overline{TP} \equiv \overline{PR} \) d) Two pairs of sides are congruent. **Explanation:** To determine if a quadrilateral is a parallelogram, we should confirm any of the following conditions: 1. Opposite sides are parallel. 2. Opposite sides are congruent. 3. Diagonals bisect each other. 4. One pair of opposite sides is both parallel and congruent. In this problem, the best choice would be based on the given criteria that can verify the presence of these conditions.
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