What is the significance of apollonius theorem

Statement and Proof by the Pythagorean Theorem. So, it is clear that. Now, use the Pythagorean Theorem. From the above equations, we can conclude that:. Hence proved. Statement and Proof by Vectors. This is a common thing getting stuck on the proof and getting confused how can you devise the solution of a problem. The best idea is to make a list of questions and try to solve them one by one to find the solution. This is always better to ask questions and experiment multiple time before you blindly cram the proof.

Connect with us. More Videos. Table of Contents. Cyclic Quadrilateral Theorem. Apollonius Theorem. Quadrilateral Theorem. Binomial Theorem. Remainder Theorem. Inscribed Angle Theorem. Angle Bisector Theorem. Pythagoras Theorem. What is Rhombus? Related Topics:. This situation is very similar to the case of a triangle.

The two sides and one diagonal form three sides of a triangle. The other diagonal is a median which bisects the first diagonal. The second diagonal is also bisected by the first. But the diagonal in parallelogram is twice the length of median of triangl e. Apollonius Theorem connects the lengths of sides of triangle, with lengths of median.

In words, it states that the sum of squares of two sides is equal to twice t he sum of squares of the median between them and half of the third side. Apollonius Theorem provides us a way of calculating median lengths in triangles , if we know their sides. This helps us solve the triangle.

The median is the line segment from one vertex to opposite side, that bisects the opposite side. The angle bisector is the line segment from one vertex to the opposite side, that bisects the angle at vertex.

In general, they are not the same , unless the vertex is between equal sides, i.