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

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