Question

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Answer 1

Answer:

Given that ABCD is a Rhombus

So AB = BC = CD = AD.

To Prove : (i) Diagonal AC bisects ∠ A as well as ∠ C.

               (ii) Diagonal BD bisects ∠ B as well as ∠ D.

Proof: (i) ABCD is a rhombus

       AD = CD ∴ ∠ DAC = ∠ DCA ...........(1)  [ Angles opposite to equal sides of a triangle are equal]

Also, CD || AB  and transversal AC intersects them ∴ ∠ DAC = ∠ BCA ..........…(2)     [Alternate Interior angles]

From (1) and (2)     ∠ DCA = ∠ BCA

⇒ AC bisects ∠ C

Similarly AC bisects ∠ A.

(ii)similarly as above, prove that BD bisects ∠ B as well as ∠ D.

Answer 2

Hope you understand..