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ABCD is a rectangle in which diagonal A...

ABCD is a rectangle in which diagonal AC bisects `/_A`as well as `/_C`. Show that:
(i) ABCD is a square
(ii) diagonal BD bisects `/_B`as well as `/_D.`.

Text Solution

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(i) As `ABCD` is a rectangle and `AC` bisects `/_A` and `/_C`,
`:. /_DAC = /_BAC and /_ACD = /_ACB`
As opposite sides of the equal angles are equal,
`:. CD = BC and AD = AB`
As `ABCD` is a rectangle,
`:. AB = CD = BC = AD`
So, `ABCD` is a square.
(ii) In `Delta ABD and Delta CBD`,
...
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