Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
Answers
Answer:
the ray BE and the ray BF are perpendicular to each other.
Step-by-step explanation:
construction 1)Draw a linear pair of angles and label them as ABD and DBC.
2)Draw an arc of sufficient radius, intersecting the ray BA, ray BD and the ray BC at points G,H and I respectively.
3)With centre, I and radius greater than half of HI draw an arc inside of DBC.
4)With centre G and the same radius draw an arc inside of ABD.
5)With centre H and the same radius, draw two arcs one on each side of the ray BD and intersecting the arc drawn in STEP 3 at F and the arc drawn in 4) point at E.
6)Draw the ray BE and the ray BF.
Answer- 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.
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