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Theorems on Quadrilaterals Ch-8 Class-IX

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  Theorems on Parallelograms Ch-8 Class-IX Explanation of all theorems on Parallelograms chapter 8 class IX, Theorem 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10, Mid point theorem and its converse. All theorems of chapter 8 class IX. Theorem 8.1: Prove that a diagonal of a parallelogram divides it into two congruent triangles. Given: In Parallelogram ABCD, AC is the diagonal To Prove:  △ACD ≌ △ABC Proof: In △ACD and △ABC,  ∠1 = ∠2  .........   (Alternate angles ∠3 = ∠4  ..........  (Alternate interior angles AC = AC ........   (Common Sides ⇒ By ASA  ≌ rule   △ACD ≌ △ABC   Theorem 8.2: In a parallelogram, opposite sides are equal. Given: ABCD is a parallelogram To Prove : AB = CD and BC = AD Proof:  In △ ACD and △ ABC,  ∠ 1 = ∠ 2  .........   (Alternate angles ∠ 3 = ∠ 4  ..........  (Alternate interior angles AC = AC ........   (Common Sides ⇒ By ASA  ≌ rule   △ ACD ≌ △ ABC ⇒ AB = CD and BC = AD  …..  By CPCT Theorem

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