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