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  • ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (ii) diagonal BD bisects ∠ B as well as ∠ D.

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

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best_answer

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.

           

Posted by

seema garhwal

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