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Answer:
The answer is given below
Step-by-step explanation:
From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.
The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠BYZ and ∠DZY are interior angles.
∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)
∠BYZ/2 + ∠DZY/2 = 180/2
∠BYZ/2 + ∠DZY/2 = 90°
In ΔOYZ:
∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).
But ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180
90 + ∠YOZ = 180
∠YOZ = 180 - 90
∠YOZ = 90°
Therefore Angle bisectors of the same side interior angles are perpendicular.
