Q6 of 45 Page 164

Let and be two straight lines intersecting at O. Let be the bisector of ∠BOD. Draw between and such that ⊥ . Prove that bisects ∠DOA.

8.JPG


Let, ∠BOX= ∠DOX = k°


According the figure,


∠BOD + ∠AOD = 180°


According the problem,


∠XOY =90° ⇒ ∠XOD + ∠YOD = 90° ⇒ ∠YOD = 90° -k°


∴ ∠BOX + ∠AOY = 90°


∠AOY = 90°- k°


∴ ∠AOY = ∠YOD


OY bisects ∠AOD


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