Q. 315.0( 3 Votes )
Prove that the bisectors of the angles of a linear pair are at right angles.
Given, ∠ACD and ∠BCD are linear pairs
CE and CF bisect ∠ACD and ∠BCD respectively
∠ECF = 90°
⸫ ∠ACD + ∠BCD = 180° [Angle on a straight line]
⇒ ∠ACD/2 + ∠BCD/2 = 180°/2 = 90°
⇒ ∠ECD + ∠DCF = 90° [⸪ CE and CF bisect ∠ACD and ∠BCD respectively]
⸫ ∠ECD + ∠DCF = ∠ECF = 90°
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