Determine which is the larger side or base of an obtuse isosceles triangle?

Since an isosceles triangle is obtuse, i.e. the angle of the vertex is greater than 90 °, then the side will always be less than the base.

If the apex angle of the triangle is greater than 90 °, then the base angles will each be less than 45 °.

Let us omit the height K from the vertex B of the isosceles triangle ABC (it will also be the median, AC = 2AK), then AK = 1/2 AB * cos <A.

The cosines of the angles, we are talking about the angles A and C at the base of an isosceles triangle ABC greater than 0 less than 45 ° are always strictly less than 1, and when multiplying 1/2 by such a number will always be strictly less than 1/2, i.e.

AK <1/2 AB.

2AK <AB

AC <AB, as required.