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ERIC Number: EJ1157084
Record Type: Journal
Publication Date: 2017
Pages: 9
Abstractor: As Provided
ISSN: ISSN-0020-739X
Understanding the Hierarchical Classification of Quadrilaterals through the Ordered Relation According to Diagonal Properties
Kabaca, Tolga
International Journal of Mathematical Education in Science and Technology, v48 n8 p1240-1248 2017
This article's aim is to suggest a supplementary learning environment to understand the hierarchical classification of quadrilaterals for high school or higher degree learners. Three diagonal properties, "being congruent, being perpendicular" and "dividing each other in particular ratio," and all possible combinations of these properties, were used to construct the quadrilaterals in a dynamic geometry environment. According to the diagonal properties, 15 quadrilaterals could be constructed and an order relation was constituted on 16 quadrilaterals including the quadrilateral that did not have any diagonal property. The definition of order relation is "any quadrilateral Qi is included by another quadrilateral Qj, if and only if Qi has all diagonal properties of Qj." According to this relation, an ordered relation diagram was created, and it was found that this relation was not well ordered. After the dynamic geometry construction of each quadrilateral, observations about the diagonal properties of special quadrilaterals were noted. Furthermore, the conditions under which a quadrilateral can be concave are examined. This alternative approach to the construction of quadrilaterals provided an opportunity to define quadrilaterals with more economical and less confusing way than using angle and side properties. For example, "a Kite is a quadrilateral whose diagonals are perpendicular and at least one of the diagonals bisects the other" and "a Trapezoid is a quadrilateral whose diagonals divide each other in same ratio."
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A