Question

Two parallel line l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

Answer 1

$Al,BL$ are bisector of $p$ & $l$

$AM,BM$ are bisector of $p$ & $m$.

Note that $AL\parallel BM$ & $BL\parallel AM$

$\Rightarrow BL=AM$ (shortest distance between $\parallel$ lines, $AL,BM$)

Similarly $AL=BM$ ($\because BL\parallel AM$)

$\therefore ALBN$ is a rectangle