Triangle where all 3 sides are the same and all angles are 60 degrees.
An equilateral triangle has all three sides equal and all three angles equal to 60°.
All sides are congruent.
All angles measure 60°.
The triangle is both equilateral and equiangular.
Equilateral triangles often appear in geometry problems involving special ratios, area formulas, or coordinate geometry. Knowing their fixed side–angle relationships allows for quick calculations without re-deriving properties.
Triangle where 2 sides are the same. 45-45-90 is a special right triangle whose side relationships are on the reference sheet.
An isosceles triangle has exactly two sides of equal length.
A special case is the 45°-45°-90° right triangle, which follows fixed side ratios (see reference sheet).
Two sides are congruent.
Angles opposite those sides are also congruent.
For a 45°-45°-90 triangle, the sides follow the ratio:
1 : 1 : \sqrt{2}
Knowing isosceles properties helps quickly find missing sides or angles. Recognizing special right triangles (like 45°-45°-90°) allows rapid calculation using standard ratios without complex work.
