A 4 sided trapezoid can also be transformed into a 4 sided isosceles trapezoid which will have equal base angles and 1 line of symmetry. Both have a pair of opposite parallel sides of different lengths.
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When you draw a diagonal in a rectangle or a parallelogram, it divides the shape into two congruent triangles, meaning both triangles are the same size and shape. In contrast, drawing a diagonal in a trapezoid results in two triangles that can differ in size and shape, as the bases of the trapezoid are unequal. Thus, different size and shape triangles form only in the trapezoid.
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Only as in the form of an isosceles trapezoid are its diagonals congruent.
They could be, but to form a trapezoid, They doesn't have to be. The legs of the trapezoid can be any length, so long as the the bases are parallel to one another.
A trapezoid has no lines of symmetry unless it is in the form of an isosceles trapezoid which has one line of symmetry