# Category: Geometry

## 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 on Triangles with Proportional Sides

This is the second in the series of posts about important and useful theorems in secondary school geometry. The first set of theorems is about angles of triangles. This second set involves the proportional sides of similar triangles. Proofs and sample problems will be provided in the next few posts. Definition: Similar Triangles Two triangles are similar

## 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