Euclidian Geometry and Conic Sections

IB Higher Level Mathematics : Option

13.1: Principles of geometric proof; postulates, theorems and their proof; deductive reasoning; if-then statements and their converses; inductive reasoning; geometric patterns.
13.2: Triangles; medians; altitudes; angle bisectors; perpendicular bisectors of sides. Concurrency; orthocentre; incentre; circumcentre; centroid. Principles of construction of triangles from secondary elements using a straight edge and compass. Euler's circle (the nine point circle).
13.3: Proportional length and proportional division of a line segment (internal and external); the harmonic ratio; proportional segments in right angled triangles. Euclid's theorem for proportional segments in a right angles triangle.
13.4: Circle geometry: tangents; chords and secants; the tangent-secant and secant-secant theorems; the intersecting-chords theorem; loci and constructions; inscribed and circumscribed polygons; properties of cyclic quadrilaterals.
13.5: Appolonius' theorem; Menelaus' theorem; Ceva's theorem; Ptolemy's bisector theorem. Proof of these theorems. The use of the theorems to prove further results.
13.6: Conic sections: focus and directrix; eccentricity. Circle; parabola; hyperbola; ellipse. Parametric equations; the general equation of second degree; rotation of axes.

13. Euclidean Geometry and Conic Sections