A Direct Proof of the Theorem: If a Line Divides Two Sides of a Triangle Proportionally, Then it is Parallel to the Third Side

Abstract

Background: The title theorem is the converse of: If a line intersects two sides of a triangle and is parallel to the third side then it divides the two sides proportionally. Our high school geometry textbook made a proof for the commensurable case and assumed the incommensurable case. The title theorem was then proved by indirect proof. As an inexperienced teacher, I didn't know enough geometry,

Thinking of deduction level students in proving theorem of triangle and its convers based on the steps of Polya

“…Buktikan teorema berikut ini. "Jika sebuah garis membagi sebanding dua sisi segitiga, maka garis itu sejajar dengan sisi ketiganya" (Todd, 2010).…”