Question

In Fig 8.120, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC = ∠DEF.

Answer 1

In Fig 8.120, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF.

Hence it is proved that ∠ABC = ∠DEF.

Construction: produce BC to x such that it intersects DE at M.

Given,

AB ║ DE   (given)

BC ║ EF   (given)        

∴ ∠ ABC = ∠ DMX ............(1)           (corresponding angles)

BX ║ EF    (from the figure)

∴ ∠ DMX = ∠ DEF ..............(2)         (corresponding angles)

From (1) and (2), we have

⇒ ∠ ABC = ∠ DEF

Hence the required proof.