No, not all angles in a trapezoid are congruent. A trapezoid may have two pairs of congruent angles, or may have no congruent angles.
Trapezoid.
A trapezoid.
By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.
A parallelogram has two pairs of sides that are parallel when a trapezoid only has one. A parallelogram's opposite sides are congruent and opposite angles are congruent. A trapezoid has no opposite congruent sides or angles, unless it's an isosceles trapezoid, which base angles are congruent. They both have four sides and four interior angles that add up to 360 degrees.
No, not all angles in a trapezoid are congruent. A trapezoid may have two pairs of congruent angles, or may have no congruent angles.
There are two pairs of congruent base angles in an isosceles trapezoid.
a rectangle
Trapezoid.
It can have 2 right angles but normally none unless it is an isosceles trapezoid in which case it will have 2 pairs of congruent base angles
rectangle
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
A trapezoid.
Adjacent angles
By definition, all trapezoids must have one pair of parallel sides. Therefore, an isosceles has one pair of congruent angles.
A parallelogram has two pairs of sides that are parallel when a trapezoid only has one. A parallelogram's opposite sides are congruent and opposite angles are congruent. A trapezoid has no opposite congruent sides or angles, unless it's an isosceles trapezoid, which base angles are congruent. They both have four sides and four interior angles that add up to 360 degrees.
Two pairs of adjacent sides are congruent. The angles between the non-congruent sides are congruent.