Can the angle at the base of an isosceles triangle be 90 degrees?

Suppose there is an isosceles triangle with a base angle of 90 °.

An isosceles triangle has two equal angles at the base, which means that the second angle of this isosceles triangle must also be 90 °.

The sum of these two angles at the base of an isosceles triangle is 90 ° + 90 ° = 180 °, therefore, the straight lines passing through the sides of the angles perpendicular to the base of the triangle are parallel.

Since the straight lines passing through these sides are parallel, they do not intersect and, therefore, such a triangle does not have a vertex that does not belong to the base.

Therefore, an isosceles triangle with a 90 ° angle at the base does not exist.