Chapter 3.3, Problem 30WE

To determine

Toprove: If two lines are parallel then bisectors of the corresponding angles are equal

Explanation of Solution

Proof:

  

Here, $l\parallel m$ and $\angle ABC,\angle BDE$ are corresponding angles.

So,

  $\angle ABC=\angle BDE$ (i)

(Corresponding angles are equal)

As BG bisects $\angle ABC$ , $\angle ABC=2\angle ABG$ (ii)

As $DF$ bisects $\angle BDE$ , $\angle BDE=2\angle BDF$ (iii)

From (i), (ii) and (iii),

  $\begin{array}{l}2\angle ABG=2\angle BDF\\ \Rightarrow \angle ABG=\angle BDF\end{array}$

Here, $\angle ABG,\angle BDF$ are corresponding angles.

So,

  $BG\parallel DF$

(Lines are parallel as corresponding angles are equal)

Hence, it can be concluded that bisectors of corresponding angles are also equal.