Geometric figures have properties. For example an isosceles triangle has two congruent sides and two congruent angles. One way in which these properties might be established is by measurement. But it is not possible to draw ALL possible isosceles triangles, nor is it possible to measure the properties of all of these triangles. To do this we need the processes of Deductive Geometry. 4 Solving geometry problems deductively Solving deductive geometry problems can involve three separate but related sets of skills and understandings: Translating a problem expressed in into a geometric diagram. A diagram can be very helpful in providing clues as to how to assemble the geometric facts to get a solution. Assembling the given facts and the related geometric theorems to get a solution. Setting down the solution, using standard geometric notation and symbols, so that someone else can come to understand how the problem has been solved. I now intend to examine each of these three aspects. In so doing I intend to offer advice as to how help students achieve high levels of competence. I also intend to draw attention to common pitfalls and common examples of poor practice. Example 1: Two circles C1 and C2 meet at the points A and B. CD is a common tangent to these circles where C and D lie on the circumferences of C1 and C2 respectively. CA is the tangent to C2 at A. When extended (produced), DB meets the circumference of C1 at P. Prove that PC is parallel to AD.
Geometric figures have properties. For example an isosceles triangle has two congruent sides and two congruent angles. One way in which these properties might be established is by measurement. But it is not possible to draw ALL possible isosceles triangles, nor is it possible to measure the properties of all of these triangles. To do this we need the processes of Deductive Geometry. 4 Solving geometry problems deductively Solving deductive geometry problems can involve three separate but related sets of skills and understandings: Translating a problem expressed in into a geometric diagram. A diagram can be very helpful in providing clues as to how to assemble the geometric facts to get a solution. Assembling the given facts and the related geometric theorems to get a solution. Setting down the solution, using standard geometric notation and symbols, so that someone else can come to understand how the problem has been solved. I now intend to examine each of these three aspects. In so doing I intend to offer advice as to how help students achieve high levels of competence. I also intend to draw attention to common pitfalls and common examples of poor practice. Example 1: Two circles C1 and C2 meet at the points A and B. CD is a common tangent to these circles where C and D lie on the circumferences of C1 and C2 respectively. CA is the tangent to C2 at A. When extended (produced), DB meets the circumference of C1 at P. Prove that PC is parallel to AD.
Teaching-Deductive-Geometry.docx