Question

In the figure, arms BA and BC of $\angle ABC$ are respectively parallel to arms ED and EF of $\angle$ DEF. Prove that $\angle ABC=\angle DEF$.

Answer 1

Given: In $\angle ABCand\angle DEF$. Their arms are parallel such that BA ||ED and BC||EF
To prove: $\angle ABC=\angle DEF$
Construction: Produce BC to meet DE at G
Proof AB|| DE
$\therefore \angle ABC=\angle DGH$ ...(i)
(Corresponding angles)
\because BC or BH|| EF
$\therefore \angle DGH=DEF$ ...(ii)
(Corresponding angles)
From (i) and (ii)
$\angle ABC=\angle DEF$