In the below fig, arms BA and BC of `∠`ABC are respectively parallel to arms ED and EF of
`∠`DEF. Prove that `∠`ABC = ∠DEF.
Given AB || DE and BC ||lry EF
To prove: `∠`ABC = `∠`DEF
Construction: Produce BC to x such that it intersects DE at M.
Proof: Since AB || DE and BX is the transversal
∴`∠`ABC = `∠`DMX [Corresponding angles] ……..(ii)
BX || EF and DE is the transversal
∴`∠`DMX = `∠`DEF [Corresponding angles] ……..(ii)
From (i) and (ii)
∴ABC = `∠`DEF
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