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The Elements
All propositions

Proposition I.5

Pons asinorum

In isosceles triangles the angles at the base are equal to one another.

Called the bridge of asses — the first proof that separates those who will follow Euclid from those who will not. The base angles of an isosceles triangle are equal. The argument is a study in corresponding parts.

Step 1 of 5

An isosceles triangle

Given

Let ABC be isosceles with AB equal to AC, and let the base be BC. We must show that angle ABC equals angle ACB.