(8) Prove that if both pairs of opposite sides of a quadrilateral are equal,
then it is a parallelogram
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what do you mean please tell me
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because it is a
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Given: A quadrilateral ABCD in which
To Prove: ABCD is a parallelogram i.e., AB ║ DC and AD║ BC
Construction : Join A and C
Proof : In ∆ABC and ∆CDA
AB = DC [Given]
AD = BC [Given]
AC = AC [Common]
∴ ∆ABC ≅ ∆CDA [By SSS]
⇒ ∠1 = ∠3 [By cpctc] And ∠2 =∠4 [By cpctc]
But these are alternate angles and whenever alternate angles are equal, the lines are parallel.
∴ AB ║ DC and AD ║ BC
⇒ ABCD is a parallelogram.
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