Question

In the below fig, arms BA and BC of `∠`ABC are respectively parallel to arms ED and EF of
`∠`DEF. Prove that `∠`ABC = ∠DEF.

Answer 1

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)

Also,

BX || EF and DE is the transversal

∴`∠`DMX = `∠`DEF     [Corresponding angles]           ……..(ii)

From (i) and (ii)

∴ABC = `∠`DEF