Question

In figure 7, OD is the bisector of angle AOC, OE is the bisector of angle BOC and OD is perpendicular to OE. Show that the points A,O and B are collinear.

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Answer 1

Answer:

<AOB=180 degree according to figure. <AOD+<DOC+<COE+<EOB=2x90 degrees...hence A,O<B are collinear.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

∠AOC + ∠COB = 2 ∠DOC +2 ∠COE ⇒ ∠AOC +∠COB = 2(∠DOC +∠COE)

⇒ ∠AOC + ∠COB= 2 ∠DOE

⇒ ∠AOC+ ∠COB = 2 x 90° [∴ OD ⊥ OE]

⇒ ∠AOC + ∠COB = 180°

∴ ∠AOB = 180°

So, ∠AOC and ∠COB are forming linear pair.

Also, AOB is a straight line.