Question

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and equals to EA=ED prove that AB is parallel to BC and EB=EC

Answer 1

$\large{\sf{Question}}$

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and equals to EA=ED prove that AB is parallel to BC and EB=EC

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$\large{\sf{Answer}}$

EB = EC and AB // BC

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$\huge \pink{ \mid \underline{ \overline{ \sf Brainly \: Solution :}} \mid}$


Given that, ABCD is a cyclic quadrilateral in which

(i) Since,

EA = ED

Then,

∠EAD = ∠EDA (i) (Opposite angles to equal sides)

Since, ABCD is a cyclic quadrilateral

Then,

∠ABC + ∠ADC = 180°

But,

∠ABC + ∠EBC = 180° (Linear pair)

Then,

∠ADC = ∠EBC (ii)

Compare (i) and (ii), we get

∠EAD = ∠EBC (iii)

Since, corresponding angles are equal

Then,

BC ‖ AD

(ii) From (iii), we have

∠EAD = ∠EBC

Similarly

∠EDA = ∠ECB (iv)

Compare equations (i), (iii) and (iv), we get

∠EBC = ∠ECB

EB = EC (Opposite angles to equal sides)