Question

Two straight lines intersect at a point. Show that the bisectors of the four angles
thus formed are equivalent to two mutually perpendicular straight lines.​

Answer 1

Answer:

Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠ AOC.

To prove : OQ is the bisector of ∠ BOD

Proof :

AB, CD and PQ are straight lines which intersect in O.

∠ AOP = ∠ BOQ (vertically opposite angles)

∠ COP = ∠ DOQ (vertically opposite angles)

∠ AOP = ∠ COP (OP is the bisector of ∠ AOC)

∴ ∠ BOQ = ∠ DOQ

Thus, the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Similarly, the bisector of ∠ AOD also bisects the ∠ BOC.

Step-by-step explanation: