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Prove that the diagonals of trapezium …

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Prove that the diagonals of trapezium intersects each other in the same ratio?

Posted by Rajdev Attri 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given in the quadrilateral ABCD
{tex}\frac{AO}{BO}=\frac{CO}{DO}{/tex}
or, {tex}\frac { A O } { C O } = \frac { B O } { D O }{/tex} ...(i)
Draw EO {tex}\parallel{/tex} AB on

In {tex}\triangle A B D,{/tex} EO {tex}\parallel{/tex} AB (By construction)
{tex}\therefore {/tex} {tex}\frac { A E } { E D } = \frac { B O } { D O }{/tex} (By BPT)...(ii)
From (i) and (ii) we get
{tex}\frac{AO}{CO}=\frac{AE}{ED}{/tex}
Hence by converse of BPT in {tex}\triangle{/tex}ADC
{tex}EO\|CD{/tex}
But {tex}EO \|AB {/tex}
So {tex}AB\|CD {/tex}
Therefore ABCD is a trapezium

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Don't post personal information, mobile numbers and other details.
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CBSE > Class 10 > Mathematics