Theorem 9.1 - Class 9th - Parallelograms on same base and between same parallels are equal in area - Paralleograms with same base & same parallel lines

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  1. Chapter 9 Class 9 Areas of parallelograms and Triangles
  2. Serial order wise
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Theorem 9.1 Parallelograms on the same base and between the same parallels are equal in area. Given : Two parallelograms ABCD & EFCD, that have the same base CD & lie between same parallels AF & CD. To Prove : 𝑎r (ABCD) = 𝑎r (EFCD) Proof : Since opposite sides of parallelogram are parallel Also, AD = BC In∆ AED and ∆ BFC ∠DAB = ∠CBF ∠DEA = ∠CFE AD = BC ∴ ∆AED ≅ Δ BFC ∴ ∆AED ≅ Δ BFC Hence, 𝑎r (∆AED) = 𝑎r (∆ BFC) Now, 𝑎r (ABCD) = 𝑎r (∆ADE) + 𝑎r(EBCD) = 𝑎r (∆BFC) + 𝑎r (EBCD) = 𝑎r (∆ EFCD) Hence, proved

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