Triangles for Math Olympiad: Complete Preparation Guide

Triangles are arguably the most important geometric topic in Math Olympiads. Congruence criteria, similarity, the Basic Proportionality Theorem, and Pythagoras theorem — these concepts appear in nearly every competition paper.

For Class 9-10 students, Olympiad triangle problems require combining multiple concepts. A single problem might test congruence, similarity, and Pythagoras — all in one elegant chain of reasoning.

Mistakes:

* Congruence vs similarity — Congruent = same size and shape. Similar = same shape, possibly different size.
* Corresponding parts — In congruent/similar triangles, match vertices in the correct order.
* BPT direction — BPT applies when a line is parallel to one side. The converse also holds.
* Pythagorean converse — If $a^2 + b^2 = c^2$, the triangle IS right-angled. If $a^2 + b^2 > c^2$, it is acute.

Try these!