Question

If a transversal intersects two lines such that the bisectors of corresponding angles are parallel, then prove that the two lines are parallel.

Answer 1

Answer:

If EB and GC are bisectors of angles ABQ and BCS then

Angles ABE =BCG eqn 1

Angles EBQ=GCS eqn 2 (as the LINES EB and GC are parallel)

adding both equations we get

ABE+EBQ=BCG+GCS

ABQ=BCS(These are corresponding angles on lines PQ AND RS)

So these lines PQ and RS are parallel