Question

two parralel l and m are intersected by a transversal p. show that the quadrilateral formed by bisectors of interior angles is a rectangle.

Answer 1

Given: L||M and P is the transversal               (if u need the image of fig. u can ask for it)

To proof: PQRS  is a rectangle
Proof:( take the quad as ABCD and the bisectors as PQRS resp)
          RS,PS,PQ and RQ are bisectors resp.
angle RSP=angle RPQ (alternate angles)
hence RS||PQ
similarly PS||RQ (angles RSP = angle PRQ)
therefore, PQRS is a ||gm
now when the angles of the bisectors are added they are 180
angle b+b = 90 and c+c=90
so, a+b= 90
one angle of pqrs is 90 degree so, it is a rectangle.
           hence proved