Question

Question 5
In the figure, BA || ED and BC || EF. Show that $\angle ABC=\angle DEF$.

Answer 1

Given, BA || ED and BC || EF.
To show $\angle ABC=\angle DEF$,
Construction:
Draw a ray EP opposite to ray ED.

Proof:
In the figure, BA || ED || DP.
$\therefore \angle ABP=\angle EPC$ [corresponding angles]
$\Rightarrow \angle ABC=\angle EPC$ . . . (i)
Again, BC || EF or PC || EF
$\therefore \angle DEF=\angle EPC$ [corresponding angles]…(ii)
From equations (i) and (ii),
$\angle ABC=\angle DEF$