An isosceles triangle has three interior angles whose base angles are equal.
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The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.
legs of an isosceles triangle
Triangle
The only requirement for an isosceles triangle is that two sides be the same length and one be different. It is possible for an isosceles triangle to have two perpendicular legs. It would be right and isosceles.
If the trapezoid is an isosceles trapezoid, with congruent legs, then the base angles are congruent. Otherwise, no.