# Tag: theorems

## Squares, Triangles, and Van-Aubel’s Theorem

Problem In the figure, H is the midpoint of side BC of ΔABC. The points I and J are the intersection of the diagonals of square ABDE and square ACGF respectively, that is they are the centers of the square. Prove that IH and HJ are congruent and that angle IHJ is a right angle.

## Theorems on Centroid, Orthocenter, and Circumcenter

Here are three important theorems involving centroid, orthocenter, and circumcenter of a triangle. This is part of the series of posts on theorems in secondary school geometry. Proofs of the theorems and application problems will be provided in the next few posts. Theorem: Centroid Theorem The lines joining the vertices of a triangle to the

## Theorems and Problems on Angles of Triangles

Here are three important theorems about triangles: sum of angles of a triangle, the measure of the exterior angle, and the base angles of an isosceles triangle. Sample problems where these are applied are also provided. The problems involved the concept of ratio. Theorem: The Sum of the Angles of a Triangle The sum of