Difference between revisions of "Gems of Geometry"
(→Concept Lecture) |
(→Concept Lecture) |
||
| Line 41: | Line 41: | ||
[https://youtu.be/taG2R4pnKec/ Session # 19] : Construction of a Nine-Point Circle using GeoGebra | [https://youtu.be/taG2R4pnKec/ Session # 19] : Construction of a Nine-Point Circle using GeoGebra | ||
| + | |||
| + | [https://youtu.be/M6vg-Lho1Wk/ Session # 20] : Theorem: The feet of the three altitudes of any triangle, the mid-points of the three sides, and the mid-points of the segments from the three vertices to the orthocenter, all lie on the same circle, of radius 1/2 R | ||
Revision as of 03:03, 13 January 2020
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
Session # 19 : Construction of a Nine-Point Circle using GeoGebra
Session # 20 : Theorem: The feet of the three altitudes of any triangle, the mid-points of the three sides, and the mid-points of the segments from the three vertices to the orthocenter, all lie on the same circle, of radius 1/2 R
