Question

5. In fig , ray AE || ray BD ray AF is the bisector of ∠EAB and ray BC is bisector of ∠ABD Prove that line AF || line BC .

Answer 1

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$\huge\bf{\underline{\underline{AnswEr}}}$

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✯ Gɪᴠᴇɴ -

Ray AE || Ray BD

Ray AF and ray BC are bisector of ∠EAB and ∠ABD

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✯ Tᴏ Pʀᴏᴠᴇ -

Ray AF || line BC

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✯ Pʀᴏᴏꜰ -

↝ Ray AE || Ray BD and AB is transversal.

↝ ∠EAB ≅ ∠ABD ... (i)... Alternate angles

↝ ∠FAB =$\frac{1}{2}$ ∠EAB ㅤㅤㅤㅤ... (ii)

ㅤㅤㅤㅤㅤㅤ ... ray AF is bisector of ∠EAB

↝ ∠ABC = $\frac{1}{2}$ ∠ABD

ㅤㅤㅤㅤㅤㅤ ... ray AF is bisector of ∠ABD

↝ ∠FAB = ∠ABC ㅤㅤㅤㅤ...from (i) (ii) and (iii)

↝ Line AF || line BC ㅤㅤㅤㅤ...Alternate Angle Test

$\huge\fbox{Hence \:Proved .}$

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