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

            (ii) diagonal BD bisects \small \angle B as well as \small \angle D.
 

Answers (1)

In \triangle ADB,

   AD = AB          (ABCD is a square)

 \angle5=\angle7.................1(angles opposite to equal sides are equal )

 \angle5=\angle8.................2 (alternate angles)

From 1 and 2, we have 

                       \angle7=\angle8.................3

   and        \angle7 =\angle6.................4(alternate angles)

From 1 and 4, we get 

                        \angle5=\angle6.................5

Hence, from 3 and 5, diagonal BD bisects angles B as well as angle D.

           

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