An Overview of Circumscribable Quadrilaterals
CHAPTER 1
INTRODUCTION
1.1 Introduction Geometry is one of the most interesting fields of mathematics. From the ancient times of the Greeks up to now, it has held captive the imagination of many mathematicians, artists, scientists, engineers and architects. Its application to modernization and technological advancement cannot be denied. Thus, it must be given emphasis in educational institutions particularly in secondary schools. The low achievement test results in mathematics of high school students in the Philippines have always been the subject of study in researches and the center of discussion in conferences. Different strategies and recourses have been drafted to be implemented in schools towards a better performance in the said subject. One such strategy is exposure to varied problems and concepts that cater to higher order thinking skills of students for them to develop critical and analytical skills. The quadrilateral is a very interesting concept for it is rich in content and applications. Quadrilaterals such as the golden rectangle and cyclic quadrilateral are famous for their intricate properties. In high schools, however, this concept is not given emphasis and teachers are confined within the types of quadrilaterals enumerated in the textbook. In effect, students’ learning is shallow. Their interests are not stimulated and they think quadrilaterals are very simple. But when given problems on quadrilaterals that are of moderate difficulty, they are stumped.
1.2 Statement of the Problem The aims of this paper are to define circumscribable quadrilaterals and to present the proofs of its properties. It also intends to discuss and prove the conditions for a quadrilateral to be circumscribable. This paper is inspired by Charles Worrall’s article entitled “ A Journey with Circumscribable Quadrilaterals” published in the Delving Deeper section of the Mathematics Teacher in October 2004. In the paper, the author explained the importance of
INTRODUCTION
1.1 Introduction Geometry is one of the most interesting fields of mathematics. From the ancient times of the Greeks up to now, it has held captive the imagination of many mathematicians, artists, scientists, engineers and architects. Its application to modernization and technological advancement cannot be denied. Thus, it must be given emphasis in educational institutions particularly in secondary schools. The low achievement test results in mathematics of high school students in the Philippines have always been the subject of study in researches and the center of discussion in conferences. Different strategies and recourses have been drafted to be implemented in schools towards a better performance in the said subject. One such strategy is exposure to varied problems and concepts that cater to higher order thinking skills of students for them to develop critical and analytical skills. The quadrilateral is a very interesting concept for it is rich in content and applications. Quadrilaterals such as the golden rectangle and cyclic quadrilateral are famous for their intricate properties. In high schools, however, this concept is not given emphasis and teachers are confined within the types of quadrilaterals enumerated in the textbook. In effect, students’ learning is shallow. Their interests are not stimulated and they think quadrilaterals are very simple. But when given problems on quadrilaterals that are of moderate difficulty, they are stumped.
1.2 Statement of the Problem The aims of this paper are to define circumscribable quadrilaterals and to present the proofs of its properties. It also intends to discuss and prove the conditions for a quadrilateral to be circumscribable. This paper is inspired by Charles Worrall’s article entitled “ A Journey with Circumscribable Quadrilaterals” published in the Delving Deeper section of the Mathematics Teacher in October 2004. In the paper, the author explained the importance of