Understand the isosceles triangle

An isosceles triangle has at least two equal sides. Here a denotes each of the equal sides and b denotes the selected base. This inclusive definition allows an equilateral triangle as a special case.

Properties that make the calculations work

The altitude from the vertex between the equal sides bisects the base and the vertex angle. The two base angles are equal. A non-degenerate triangle requires b < 2a.

Where the model is useful

A symmetric gable diagram or triangular sign can be modelled with these relationships. Choose inputs that reflect what was actually measured: side and base, base and height, vertex angle or perimeter.

Measure the right thing

Vertex angle means the angle between the equal sides. The base is not necessarily the longest side.

Sketch the figure and mark every known measurement before choosing a calculator. A length measured along an edge is not automatically a perpendicular height. If a formula needs a radius, check that the value has not been measured across a full diameter. Write the unit beside each known quantity before entering it.

Scale and units

Multiplying every length by k multiplies any area by k². This is a useful check: doubling all dimensions cannot merely double an area. Inputs expressed in centimetres produce cm² for area; the unit selector relabels rather than converts entered numbers.

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Wolfram MathWorld: Isosceles triangle provides reference reading. Our summaries and examples are written for this portal and are not a specialist-reviewed textbook. Try a worked example or suggest a correction.