If the bisector of two adjacent angles are perpendicular to one another, then prove that the adjacent angles are formed by two intersecting straight lines?

By

Let us assume that there are three intersecting lines.







Angle /_EBD+/_FBD=90°

or, 1/2(/_ABD+/_CBD)=90°

or, /_ABD+/_CBD = 180°

Therefore ABC is a straight line and AB and BC are collinear, therefore the adjacent angles are formed by the lines ABC and BD (only two lines)

Hence proved.





 

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