Question

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Interesting Question Here !!

In Quadrilateral ABCD, diagonals AC and BD intersect at point E, such that
AE : EC = BE : ED
Show that :- ABCD is a Trapezium. Kindly,

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Answer 1

★ Question :-

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In Quadrilateral ABCD, diagonals AC and BD intersect at point E. Such that

AE : EC = BE : ED

Show that :- ABCD is a Trapezium.

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★ Answer :-

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ln the above attachment, ABCD is a quadrilateral with diagonals AC and BD intersect at point E .

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⟹ ln △DEC and △AEB

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⠀⠀⠀$\sf \small{ \frac{AE}{EC} = \frac{BE}{ED}} \: \: \: .... \: \sf \small \pink{given} \\ \\ \sf \small{∠ \: DEC =∠ \: AEB } \: \: \: .... \: \sf \small \pink{vertically \: opposite\: angles} \\ \\ \sf \small{∴ \: EBA = \: ∠ \: CDE} \: \: \: .... \: \sf \small \pink{allternate \: angles} \\ \\ \sf \small{∴ \: AB \: ∥ \: DC} \\ \\ \boxed{ \sf{ \small{∴ \: Given \: Fig \: is \: { \underline \red{Trapezium }}}}}$

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$\bigstar\:\small \green{ \fcolorbox{gray}{black} {\textbf{ Hence, Proved ✔ }}}$