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Question:

In the figure, if AC=BD, then prove that AB=CD.

Solution:

Given,AC=BD... (i)AC=AB+BC……(ii) (PointBlies betweenAandC)BD=BC+CD… (iii) (PointClies betweenBandD)Now,substituting (ii) and (iii) in (i), we get⇒AB+BC=BC+CD⇒AB+BC–BC=CD⇒AB=CDHence,AB=CD.