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If Abcd is a Parallelogram, Then Prove that π‘Žπ‘Ÿ (δ𝐴𝐡𝐷) = π‘Žπ‘Ÿ (δ𝐡𝐢𝐷) = π‘Žπ‘Ÿ (δ𝐴𝐡𝐢) = π‘Žπ‘Ÿ (δ𝐴𝐢𝐷) = `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷) . - Mathematics

If ABCD is a parallelogram, then prove that
π‘Žπ‘Ÿ (Δ𝐴𝐡𝐷) = π‘Žπ‘Ÿ (Δ𝐡𝐢𝐷) = π‘Žπ‘Ÿ (Δ𝐴𝐡𝐢) = π‘Žπ‘Ÿ (Δ𝐴𝐢𝐷) = `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷) .

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Solution

Given: ABCDis a parallelogram
To prove : area  (Δ𝐴𝐡𝐷) = π‘Žπ‘Ÿ (ΔA𝐡𝐢) = are  (Δ ACD)

 = `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷)

Proof: we know that diagonals of a parallelogram divides it into two equilaterals.
Since, AC is the diagonal.

Then, π‘Žπ‘Ÿ (Δ𝐴𝐡𝐢) =   (Δ ACD) = `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷)............ (1)

Since, BD is the diagonal

Then, π‘Žπ‘Ÿ (Δ𝐴𝐡𝐢) = π‘Žπ‘Ÿ (Δ𝐡𝐢𝐷)  = `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷)............ (2)

Compare equation (1) and (2)

∴ π‘Žπ‘Ÿ (Δ𝐴𝐡𝐢) =  π‘Žπ‘Ÿ (Δ𝐴𝐢𝐷)

 = π‘Žπ‘Ÿ (Δ𝐴𝐡𝐷) =  π‘Žπ‘Ÿ (Δ𝐡𝐢𝐷) =   `1/2` π‘Žπ‘Ÿ (||π‘”π‘š 𝐴𝐡𝐢𝐷)

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.2 | Q 4 | Page 15
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