When Are the Diagonals of a Trapezium Equal?

By Team Aakash Byju's | 31st January 2023

In given figure, ABCD is a trapezium with AB||DC. If AED is similar to BEC, prove that AD = BC.

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We must note 2 things: (i) Corresponding sides of two similar triangles are in equal proportion. (ii) If 2 corresponding angles in two triangles measure the same, then the triangles are similar.

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Given, ΔAED∼ΔBEC,

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Consider triangles ΔABE and ΔCDE,

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Thus, ΔABE∼ΔCDE by AA-similarity.

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Further, because ΔAED∼ΔBEC gives

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Since,

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