Question

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.​

Answer 1

Step-by-step explanation:

As shown in the attached figure, ∠AOC and ∠BOC form a linear pair, so we have

∠AOC + ∠BOC = 180°.

Ray OP and ray OQ are drawn which bisects ∠AOC and ∠BOC respectively. We are to prove that ∠POQ = 90°.

Therefore, we have

2∠AOP = 2∠COP = ∠AOC and 2∠BOP = 2∠COQ = ∠BOC.

Now,

\begin{gathered}\angle AOC+\angle BOC=180^\circ\\\\\Rightarrow 2\angle POC+2\angle QOC=180^\circ\\\\\Rightarrow \angle POC+\angle QOC=90^\circ\\\\\Rightarrow \angle POQ=90^\circ.\end{gathered}

∠AOC+∠BOC=180

∘

⇒2∠POC+2∠QOC=180

∘

⇒∠POC+∠QOC=90

∘

⇒∠POQ=90

∘

.

Thus, the bisecting rays are perpendicular to each other. Hence verified.