Prove that the area of any quadrilateral withperpendicular diagonals =

1.	Prove that the area of any quadrilateral withperpendicular diagonals =-× Product ofdiagonals.10.
Answer» Proof :Since the diagonals AC and BD of quadrilateral ABCD bisect each other at right angles.Therefore, AC is the perpendicular bisector of the segment BD.A and C both are equidistant from B and D.AB = AD and CB = CD ... (1)Also , BD is the perpendicular bisector of line segment AC.B and D both are equidistant from A and C.AB = BC and AD = DC ... (2)From (1) and (2), we getAB = BC = CD = ADThus , ABCD is a quadrilateral whose diagonals bisect each other at right angles and all four sides are equal.Hence , ABCD is a rhombus. now it is proved tha ABCD is a rombus and area of Rombus =1/2 product of diagonals.Hence, proved

Prove that the area of any quadrilateral withperpendicular diagonals =-× Product ofdiagonals.10.

Answer»

Proof :Since the diagonals AC and BD of quadrilateral ABCD bisect each other at right angles.Therefore, AC is the perpendicular bisector of the segment BD.A and C both are equidistant from B and D.AB = AD and CB = CD ... (1)Also , BD is the perpendicular bisector of line segment AC.B and D both are equidistant from A and C.AB = BC and AD = DC ... (2)From (1) and (2), we getAB = BC = CD = ADThus , ABCD is a quadrilateral whose diagonals bisect each other at right angles and all four sides are equal.Hence , ABCD is a rhombus.

now it is proved tha ABCD is a rombus and area of Rombus =1/2 product of diagonals.Hence, proved

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