Not necessarily
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The top and bottom angles - the angles that are between the pairs of congruent sides. They are opposite each other and not necessarily congruent.
A quadrilateral that could have a 45-degree vertex angle is a kite. In a kite, the two pairs of adjacent sides are congruent, and one pair of opposite angles is congruent. Therefore, if one of the angles is 45 degrees, the opposite angle would also be 45 degrees. This makes a kite one of the quadrilaterals that could have a 45-degree vertex angle.
be congruent and have the same vertex
Both are quadrilaterals. Both have two pairs of side of equal length. In a kite they are adjacent sides, in a rectangle they are opposite. A kite has one pair of equal angles, all of a rectangle's angles are equal. In a kite, one diagonals bisects the other, in a rectangle both do.
A kite is a quadrilateral with two pairs of adjacent congruent sides. The angles between the unequal sides are equal.