Prove that the area of any quadrilateral with perpendicular diagonals is equal to half product of diagonals
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A quadrilateral ABCD in which the diagonals AC and BD intersect at O assume that AO = OC , BO = OD . AC perpendicular BD.
To prove : ABCD is a rhombus.
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 get
AB = BC = CD = AD
Thus , 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
Read more on Brainly.in - https://brainly.in/question/1421980#readmore
A quadrilateral ABCD in which the diagonals AC and BD intersect at O assume that AO = OC , BO = OD . AC perpendicular BD.
To prove : ABCD is a rhombus.
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 get
AB = BC = CD = AD
Thus , 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
Read more on Brainly.in - https://brainly.in/question/1421980#readmore
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