Last updated at April 19, 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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