# Formulas and Tables

Elementary Geometry# Isosceles Triangle

Base: \(a\)

Legs: \(b\)

Base angle: \(\beta\)

Vertex angle: \(\alpha\)

Perimeter of an isosceles triangle: \(P\)

Area of an isosceles triangle: \(S\)

- Relationship between the vertex and base angles

\(\beta = 90^\circ – {\large\frac{\alpha }{2}\normalsize}\) - Altitude drawn to the base

\({h^2} = {b^2} – {\large\frac{{{a^2}}}{4}\normalsize}\) - In an isosceles triangle, the altitude, angle bisector, median and perpendicular bisector drawn from the vertex to the base coincide.
- Relationships between the legs and the base

\(b = 2a\cos \alpha,\;\) \(b = 2a\sin {\large\frac{\beta }{2}\normalsize}\) - Perimeter of an isosceles triangle

\(P = a + 2b\) - Area of an isosceles triangle

\(S = {\large\frac{{ah}}{2}\normalsize} =\) \({\large\frac{{{b^2}}}{2}\normalsize}\sin \alpha =\) \({\large\frac{{ab}}{2}\normalsize}\sin \beta \)