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

                (i) ABCD is a square 

Answers (1)

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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