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5. In accordance with an inclusive definition, the rhombuses in the following figure are enclosed in dashed lines: For each of the possible definitions given next, de- cide whether it is a good definition (an equivalent definition) of a rhombus. If it is not equivalent, then give the number of a counterexample among the preceding figures. Possible Definition A A four-sided polygon is a rhombus if both diagonals are lines of symmetry. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition BA quadrilateral is a rhombus if each diagonal cuts it into two congruent halves. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition C A quadrilateral is a rhombus f the diagonals are perpendicular bisectors of each other. Equivalent definition? YES NO

5. In accordance with an inclusive definition, the rhombuses in the following figure are enclosed in dashed lines: For each of the possible definitions given next, de- cide whether it is a good definition (an equivalent definition) of a rhombus. If it is not equivalent, then give the number of a counterexample among the preceding figures. Possible Definition A A four-sided polygon is a rhombus if both diagonals are lines of symmetry. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition BA quadrilateral is a rhombus if each diagonal cuts it into two congruent halves. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition C A quadrilateral is a rhombus f the diagonals are perpendicular bisectors of each other. Equivalent definition? YES NO

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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Possible Definition C A quadrilateral is a rhombus 5. In accordance with an inclusive definition, the rhombuses in the following figure are enclosed in dashed lines: 3 企公 For each of the possible definitions given next, de- cide whether it is a good definition (an equivalent definition) of a rhombus. If it is not equivalent, then give the number of a counterexample among the preceding figures. Possible Definition A A four-sided polygon is a rhombus if both diagonals are lines of symmetry. NO Equivalent definition? YES If NO, give the number of a counterexample: Possible Definition B A quadrilateral is a rhombus if each diagonal cuts it into two congruent halves. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition C A quadrilateral is a rhombus u the diagonals are perpendicular bisectors of each other. ASO ples Equivalent definition? YES NO
Transcribed Image Text:Possible Definition C A quadrilateral is a rhombus 5. In accordance with an inclusive definition, the rhombuses in the following figure are enclosed in dashed lines: 3 企公 For each of the possible definitions given next, de- cide whether it is a good definition (an equivalent definition) of a rhombus. If it is not equivalent, then give the number of a counterexample among the preceding figures. Possible Definition A A four-sided polygon is a rhombus if both diagonals are lines of symmetry. NO Equivalent definition? YES If NO, give the number of a counterexample: Possible Definition B A quadrilateral is a rhombus if each diagonal cuts it into two congruent halves. Equivalent definition? YES NO If NO, give the number of a counterexample: Possible Definition C A quadrilateral is a rhombus u the diagonals are perpendicular bisectors of each other. ASO ples Equivalent definition? YES NO
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