Q. 315.0( 3 Votes )

Prove that the bisectors of the angles of a linear pair are at right angles.

Answer :


Given, ACD and BCD are linear pairs


CE and CF bisect ACD and BCD respectively


To prove:


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°


Hence Proved.


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