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Q.

In the given figure, AB and CD intersect each other at E, such that DE = BE and EA = EC. Is it true that AD = CB?


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a

True

b

False 

answer is A.

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Detailed Solution

Given, AB and CD intersect each other at E, such that DE = BE and EA = EC.
Question ImageIn △AED and △BEC,
∠AED = ∠BEC (Opposite angles are equal)
AE = CE (Given data)
DE = BE (Given data)
So, △AED ⩭ △BEC.
Thus, by CPCT ∠ADE = ∠BCE, ∠DAE = ∠CBE and AB = CB.
So, we can say that AB = CB.
So, the given statement is true and the correct option is 1.
 
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In the given figure, AB and CD intersect each other at E, such that DE = BE and EA = EC. Is it true that AD = CB?