By Anjali Amit, Updated Aug 30, 2022
A triangle is a three‑sided polygon. Understanding its various forms and the relationships between its sides and angles is essential for mastering geometry and tackling high‑stakes tests like the SAT.
Use a ruler to determine the length of each side. If all three sides are equal, the triangle is equilateral—and consequently also equiangular. Every interior angle in an equilateral triangle measures exactly 60°, regardless of side length.
Measure each angle. If all three read 60°, you’ve confirmed an equilateral (and equiangular) triangle. If not, proceed to the next step.
When exactly two sides match, the triangle is isosceles. The two angles opposite those equal sides—the base angles—are equal. For example, if one base angle is 55°, the other is also 55°, and the vertex angle is 180° – (55° + 55°) = 70°.
All equilateral triangles are a special subset of isosceles triangles. Another notable type is the right isosceles triangle, whose angles are 90°, 45°, and 45°. Knowing any one of these angles allows you to deduce the others.
A right triangle contains a single 90° angle. The side opposite this angle is the hypotenuse, while the other two sides are called the legs. The Pythagorean theorem—c² = a² + b²—holds for all right triangles. The classic 30°‑60°‑90° triangle is a key example.
If every interior angle is less than 90°, the triangle is acute. If one angle exceeds 90°, the triangle is obtuse, and the remaining two angles are acute.
