Special cases of triangles

Special triangles are those with particular relationships among their sides or angles, leading to unique properties and formulas. The most common special triangles are: equilateral triangles (all sides and angles equal), isosceles triangles (two sides and two angles equal), right triangles (one $90^ ext{o}$ angle), and triangles with angles like $30^ ext{o}$-$60^ ext{o}$-$90^ ext{o}$ or $45^ ext{o}$-$45^ ext{o}$-$90^ ext{o}$.

Important properties

• Equilateral triangle: all sides equal, all angles $60^ ext{o}$.

• Isosceles triangle: two sides and two angles equal.

• Right triangle: one angle is $90^ ext{o}$; Pythagoras' theorem applies.

• Triangles with angles $30^ ext{o}$, $60^ ext{o}$, $90^ ext{o}$ or $45^ ext{o}$, $45^ ext{o}$, $90^ ext{o}$ have fixed side ratios.