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

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.

Solution:

Given

AB ∥ DE and BC ∥ 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 angle]  .... (i)

Also, BX ∥ EF and DE is the transversal

DMX = DEF                             [Corresponding angles]         -----(ii)

From (i) and (ii)

∠ABC = ∠DEF

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