In order to derive implications for the reasoning tasks presented in Korean textbooks, this study classified tasks of the proposition of quadrilateral unit in Korean and U.S. textbooks into type of proof-related reasoning, analyzed them according to the level of reasoning and argument competency demands. In addition, detailed characteristics according to each level were examined for tasks of the types of DA, IC and MC that accounted for the majority. As a result of the analysis, low-level tasks were presented at a high rate in both countries, but the proportion of high-level tasks was higher in U.S. textbooks. Additionally, opportunities to develop reasoning and argument competency were provided at a limited level for each type of reasoning. This tendency could be clearly confirmed based on the detailed characteristics of reasoning tasks related to the proposition of quadrilateral unit in Korea, examined by the type of reasoning. Therefore Korean textbooks need to provide opportunities to learn high-level reasoning, to present tasks at various levels according to each type of reasoning furthermore, and to reconsider how to develop and transform tasks of various levels for each reasoning type in terms of element and the chain of inference.