Question

If two parallel lines are intersected by a transversal prove that the bisectors of the two pairs of interior angles enclose a rectangle

Answer 1

This is the answer of ur question

Answer 2

Refers to the attachments

GIVEN: Two parallel Lines AB and CD. EF is transversal which intersecting at G and H.

TO PROVE: GHML is a rectangle.

PROOF: <AGH=<DHG (alternate interior <'s)

=> 1/2<AGH=1/2<DHG

=>HGM=GHL

GM and HL are interested by transversal GH at G and H.

Therefore,

GH//HL

Similarly,

GL//HM

So,GMHL is a parallelogram.

Since, AB//CD and EF is transversal.

Therefore,

<BGH + <DHG =180° (sum of interior angles on the same side)

=> 1/2<BGH + 1/2<DHG =90°

=>LGH+LHG =90°

Sum of the angles of triangle is 180°

<LHG + <LGH + <GLH =180°

90°+ <GLH =180°

<GLH=90°

Therefore, GMHL is a rectangle.