Given square ABCD is a rectangle in which diagonal BD bisect angle B as well as angle D prove that ABCD is a square
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ABCD is a square
Step-by-step explanation:
a rectangle ABCD, diagonal BD bisects ∠B.
Join AC.
In △BAD and △BCD,
⇒ ∠ABD=∠CBD [ Since BD bisect ∠B ]
⇒ ∠A=∠C [ Each angle of a rectangle is 90
o
. ]
⇒ BD=BD [ Common side ]
∴ △BAD≅△BCD [ By AAS congruence rule ]
⇒ AB=BC and AD=CD [ CPCT ] ---- ( 1 )
We know opposite sides of rectangle are equal.
∴ AB=CD and BC=AD ---- ( 2 )
From ( 1 ) and ( 2 ),
⇒ AB=BC=CD=DA
∴ ABCD is a square.
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