Medians of a Triangle are Concurrent. The Point of Concurrency is the Centroid.
median of a triangle is the line joining the midpoint of a side and the opposite vertex.
Angle Bisectors of a Triangle are Concurrent. The Point of Concurrency is the Incenter.
Altitudes of a Triangle are Concurrent. The Point of Concurrency is the Orthocenter.
altitude is the perpendicular line drawn from a vertex on the opposite side of the triangle.
Perpendicular Bisectors of a Triangle are Concurrent. The Point of Concurrency is the Circumcenter.
parallelopiped is a 3-D object, each of whose faces is a parallelogram.
rectangular parallelopiped is the one, whose faces are rectangular.
cube is a rectangular parallelopiped, whose edges are of equal length.
tetrahedron is a 3-D object, whose all faces are triangular. It can be shown that a parallelopiped can be decomposed into 6 tetrahedra.
Image Source : https://www.dune-project.org/
For a visual proof :
1 Parallelopipded = 6 Tetrahedra
Let there be 2 such objects, whose coterminus edges are identical. Then, the volume of the tetrahedron is
th of that of the parallelopiped. The expression can also be obtained using the following theorem :
In this blog, we will prove fundamental theorems in vector algebra. These theorems are in accordance with the +2 curriculum.
Theorem 1 : Collinear Vectors
Theorem 2 : Non-collinear and Coplanar Vectors
Theorem 3 : Coplanar Vectors
Theorem 4 : Non-coplanar Vectors