In this 2-day FACE-to-FACE course we enter the World of Geometry, explore its objects and relations, examine propositions and proofs, using a range of simple tools and practical techniques such as paper and paperfolding, silent film, apps (GeoGebra) and animation, geoboards and more, … to reveal the elementary theorems and applications of FET geometry.

Teaching Strategy:

The approach is activity-based, using both inductive (discovery) conjecturing and justification, and deductive (more formal) reasoning and proof as models of teaching and learning. In terms of specific content, the course will focus on Grade 11 Circle Geometry, including the brief recovery of all Senior Phase geometry.

DAY 1: The World of Geometry –– points, lines, angles ad plane, assumptions, axioms and common notions, definitions and properties. In this session we introduce and use simple tools –– paper, paperfolding, trace paper, transparencies, geoboards, and simple animation to explore:

• Relationships and results involving intersecting lines, angles and triangles.
• Theorem of Pythagoras.
• Fermat’s last theorem.
• Nicolet Films and animation.
• Circle Geometry –– Conjecturing and informal (inductive) proof.

DAY 2: Formalizing propositions and theorems through deductive reasoning. In this session we have the opportunity formally prove conjectures and propositions (theorems), as we leave the inductive, discovery-based approach. We firmly establish the theorems of circle geometry and apply our deductive reasoning skills to solve geometrical problems and riders as required in Grade 11 and also applicable to Grade 12, including:

• The line drawn from the centre of a circle perpendicular to a chord bisects the chord;
• The perpendicular bisector of a chord passes through the centre of the circle;
• The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre);
• Angles subtended by a chord of the circle, on the same side of the chord, are equal;
• The opposite angles of a cyclic quadrilateral are supplementary;
• Two tangents drawn to a circle from the same point outside the circle are equal in length;
• The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment.