If one diagonal of a Trapezium …

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If one diagonal of a Trapezium divides the other diagonal in the ratio 1:3 , prove that one of the parallel sides is 3 times the other.

Posted by Kiran S B Patil 5 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 5 years, 9 months ago

DE = EB = 1:3
In $\triangle$ AEB and $\triangle$ CED, $\angle 1 = \angle 2$ (alternate angles)

$\angle 3 = \angle 4$ (Vertically opposite angles.)
$\therefore \quad \Delta \mathrm { AEB } \sim \Delta \mathrm { CED }$
$\Rightarrow \quad \frac { \mathrm { AB } } { \mathrm { CD } } = \frac { \mathrm { BE } } { \mathrm { DE } } \Rightarrow \frac { \mathrm { AB } } { \mathrm { CD } } = \frac { 3 } { 1 }$ [ $\because$ DE: BE = 1:3]
$\Rightarrow$ AB = 3CD

4Thank You

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