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

Question

In Fig 8.120, arms BA and BC of &#x2220; ABC are respectively parallel to arms ED and EF of &#x2220; DEF . Prove that &#x2220; ABC = &#x2220; DEF .

Philoid · Accepted Answer

Given that,

AB ‖ DE and EC ‖ 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

Therefore,

∠ABC = ∠DMX (Corresponding angles) (i)

Also,

BX ‖ EF and DE is transversal

Therefore,

∠DMX = ∠DEF (Corresponding angles) (ii)

From (i) and (ii), we get

∠ABC = ∠DEF

Hence, proved