Problem The two regular polygons ABCDEF and JKI have the same perimeter. What is the ratio of their areas? Solution Since you are comparing areas of polygons, the most efficient solution would be to dissect them into congruent shapes. That is, show that both polygons can be tessellated or tiled by the same shape. Of
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
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