prove that the bisectors of the angles of a linear pair are at right angles.
In the figure ∠ACD and ∠BCD form a linear pair ⇒∠ACD+∠BCD=180º
CE and CF bisect ∠ACD and ∠BCD respectively
∠ACD+∠BCD=180º
⇒∠ACD/2 + ∠BCD/2 = 90º
⇒∠ECD + ∠DCF = 90º as CE and CF bisect ∠ACD and ∠BCD respectively
⇒∠ECF = 90º (∠ECD + ∠DCF = ∠ECF)
∠ECF is the angle between CE and CF which bisect the linear pair of angles ∠ACD and ∠BCD
Hence proved that the angle bisectors of a linear pair are at right angles to each other