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ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Q.7

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Please give me the best way for solving the problem of class 9th ncert math of Quadrilaterals chapter of math of class 9th of exercise 8.1of question no 7  what is the tricky way for solving this question ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

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  1. Ncert solutions class 9 chapter 8-6

    Given that,

    ABCD is a rhombus.

    AC and BD are its diagonals.

    Proof,

    AD = CD (Sides of a rhombus)

    ∠DAC = ∠DCA (Angles opposite of equal sides of a triangle are equal.)

    also, AB || CD

    ⇒∠DAC = ∠BCA (Alternate interior angles)

    ⇒∠DCA = ∠BCA

    , AC bisects ∠C.

    Similarly,

    We can prove that diagonal AC bisects ∠A.

    Following the same method,

    We can prove that the diagonal BD bisects ∠B and ∠D.

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