ABCD is a rectangle in which diagonal BD bisects angle B.Show that a b c d is a square.
can I do it in this process
BD bisects angle B
therefore angle ABD =angle DBC
angle ABD = angle DBC( alternate angles)
each angle of rectangle is 90°
therefore ABD = 45°
similarly ADB=45°
therefore AB = AD therefore each angle is equal it is a square
Dear Student,
Please find below the solution to the asked query:
We form our diagram from given information , As :
Here , ABD = CBD = 45 --------- ( 1 ) ( We know all angles of rectangle at 90 )
And
CBD = ADB = 45 --------- ( 2 ) ( Alternate angles as we take BC | | DA and BD as transversal line )
From equation 1 and 2 we get ABD is isosceles triangle and from base angle theorem we get .
AB = AD , So
AB = BC = CD = AD
Therefore,
ABCD is a square . ( Hence proved )
Hope this information will clear your doubts about quadrilateral .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
We form our diagram from given information , As :
Here , ABD = CBD = 45 --------- ( 1 ) ( We know all angles of rectangle at 90 )
And
CBD = ADB = 45 --------- ( 2 ) ( Alternate angles as we take BC | | DA and BD as transversal line )
From equation 1 and 2 we get ABD is isosceles triangle and from base angle theorem we get .
AB = AD , So
AB = BC = CD = AD
Therefore,
ABCD is a square . ( Hence proved )
Hope this information will clear your doubts about quadrilateral .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards