Question

show that if diagonals of a quadrilateral bisect each other at right angle then it is a rhombus.

plz write the steps

Answer 1

Given-diagonals bisect each other at right angle. Take any of the two triangles and prove them congruent by taking the angle of 90,equal sides and the side in common. when the triangle proved congruent then take the adjacent side of quad. and prove them equal by CPCTs

Answer 2

if the diagonal of rhombus or of any quadrilateral bisect each other at 90°then the perpendicular and base of all the four Triangles are equal and hence the hypotenuse of all the triangle will also be equal then the all side of quadrilateral are equal and the triangle opposite to each other are concurrent to each other so all the angles are equal to each other and the sides are parallel so that quadrilateral formed is rhombus