Op bisects angle AOC and oq bisects angle boc op is perpendicular to oq prove that a o b are collinear
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Welvome
Comment
Given: OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ.To Prove: The points A, O and B are collinear.Proof: ∵ OP bisects ∠AOC∴ ∠AOP = ∠COP ...(1)∵ OQ bisects ∠BOC∠BOQ = ∠COQ ...(2)Now, ∠AOB= ∠AOP ∠COP ∠COQ ∠BOQ= ∠COP ∠COP ∠COQ ∠COQ| From (1) and (2)= 2(∠COP ∠COQ)= 2 ∠POQ= 2(90°) | ∵ OP ⊥ OQ= 180°∴ The points A, O and B are collinear.| By converse of Linear Pair
Answer the question...
Welvome
Comment
Given: OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ.
To Prove: The points A, O and B are collinear.
Proof: ∵ OP bisects ∠AOC
∴ ∠AOP = ∠COP ...(1)
∵ OQ bisects ∠BOC
∠BOQ = ∠COQ ...(2)
Now, ∠AOB
= ∠AOP ∠COP ∠COQ ∠BOQ
= ∠COP ∠COP ∠COQ ∠COQ
| From (1) and (2)
= 2(∠COP ∠COQ)
= 2 ∠POQ
= 2(90°) | ∵ OP ⊥ OQ
= 180°
∴ The points A, O and B are collinear.
| By converse of Linear Pair