Gems of Geometry

Concept Lecture

Session # 01 : The Laws of Sine

Session # 02 : Ceva's Theorem

Worksheet # 01 : Worksheet on Sine Law and Ceva's Law

Session # 03 : Stewart's Theorem

Session # 04 : Medians of a triangle divide it into six parts of equal areas.

Session # 05 : Medians of a triangle trisect each other

Session # 06 : Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides. Proof using Sine Rule

Worksheet # 02 : Worksheet on Stewart's Theorem and properties of medians of a triangle

Session # 07 : The area of a triangle is equal to the product of the semi-perimeter and the in-radius

Session # 08 : The locus of a point equidistant from two intersecting lines is the angle bisector of the angle between the intersecting lines.

Session # 09 : Theorem: The external bisectors of any two angles of a triangle are concurrent with the internal bisector of the third angle

Session # 10 : Some properties of ex-circles and in-circle of a triangle

Session # 11 : If two chords of a circle subtend different acute angles at points on the circle, the smaller angle belongs to the shorter chord.

Session # 12 : In a triangle, the angle bisector of the smaller angle is greater than the angle bisector of the greater angle

Session # 13 : The Steiner-Lehmus Theorem : Any triangle that has two equal angle bisectors (each measured from a vertex to the opposite side) is isosceles.

Session # 14 : The orthocenter of an acute-angled triangle is the in-center of its orthic triangle.

Session # 15 : What is a medial triangle? What is an Euler Line in a triangle?

Session # 16 : Centroids of a triangle and its medial triangle are coincident

Session # 17 : The Circumcenter of a Triangle and the Orthocenter of its Medial Triangle are coincident

Session # 18 : The orthocenter, centroid and circumcenter of any triangle are collinear. The centroid divides the distance from the orthocenter to the circumcenter in the ratio 2:1