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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 (2)

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Yesterday i was doing the question from class 9th ncert book of math of Quadrilaterals chapter of exercise 8.1  What is the easiest way for solving it because i was not able to do this question please help me for solving this question of 8.  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.

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  1. Ncert solutions class 9 chapter 8-7

    (ii) In ΔBCD,

    BC = CD

    ⇒ ∠CDB = ∠CBD (Angles opposite to equal sides are equal)

    also, ∠CDB = ∠ABD (Alternate interior angles)

    ⇒ ∠CBD = ∠ABD

    Thus, BD bisects ∠B

    Now,

    ∠CBD = ∠ADB

    ⇒ ∠CDB = ∠ADB

    Thus, BD bisects ∠D

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