Theorem 8.5
Last updated at Nov. 23, 2017 by Teachoo
Transcript
Theorem 8.5 If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral with opposite angles equal, i.e. ∠ 1 = ∠ 3 & ∠ 2 = ∠ 4 To Prove : ABCD is a Parallelogram Proof : By angle sum property of quadrilateral ∠1 + ∠2 + ∠3 + ∠4 = 360° ∠1 + ∠2 + ∠1 + ∠2 = 360° 2(∠1 + ∠2) = 360° ∠1 + ∠2 = 360°2 ∠1 + ∠2 = 180° Similarly we can prove that, ∠1 + ∠4 = 180° Thus, In ABCD, Both pairs of opposite sides are parallel, ∴ ABCD is a parallelogram
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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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Hii
Can't we prove theorem 8.5 using theorem 8.1 that states ' diagonal of a paralleogram divides it into two congruent triangles" ?
I meant to say :
1.Draw the diagonal
2.Based on given data, prove that 2 triangles are congruent.
3.Atlast say " as the diagonal divides the given figure into two congruent triangles it is a paralleogram."
Is my method correct??
