If you mean an isosceles triangle then no because all triangles have no diagonals
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yes! But only an isosceles Trapezoid.
Only as in the form of an isosceles trapezoid are its diagonals congruent.
A trapezoid with congruent diagonals is an isosceles trapezoid.
Yes They are always congruent to each other.
Only the diagonals of isosceles trapezoids are congruent.