# Category: Theorems in Geometry

## Three proofs that the sum of angles of a triangle is 180

Theorem. The sum of the interior angles of any triangle is 180°. Here are three proofs for the sum of angles of triangles. Proof 1 uses the fact that the alternate interior angles formed by a transversal with two parallel lines are congruent. Proof 2 uses the exterior angle theorem. Proof 3 uses the idea

## 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