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  • ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (i) ABCD is a square.

Q: 8 ABCD is a rectangle in which diagonal AC bisects \small \angle A as well as \small \angle C. Show that ABCD is a square 

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Given: ABCD is a rectangle with AB=CD and BC=AD \angle1=\angle2 and \angle3=\angle4.

 To prove: ABCD is a square.

Proof :     \angle1=\angle4 .............1(alternate angles)

  \angle3=\angle4 ................2(given )

  From 1 and 2, \angle1=\angle3.....................................3

    In \triangleADC,

   \angle1=\angle3          (from  3 )   

    DC=AD   (In a triangle, sides opposite to equal angle are equal )

A rectangle whose adjacent sides are equal is a square.

Hence, ABCD is a square.

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