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

Answer: Verified.

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,

$\angle AOC+\angle BOC=180^\circ\\\\\Rightarrow 2\angle POC+2\angle QOC=180^\circ\\\\\Rightarrow \angle POC+\angle QOC=90^\circ\\\\\Rightarrow \angle POQ=90^\circ.$

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

Answer 2

Draw a linear pair of angles and label them as and . Draw an arc of sufficient radius, intersecting the ray , ray and the ray at points G,H and I respectively.

• With centre, I and radius greater than half of HI draw an arc inside of. With centre G and the same radius draw an arc inside of.

• With centre H and the same radius, draw two arcs one on each side of the ray and intersecting the arc drawn in.

STEP 3 at and the arc drawn in

STEP 4 at . Draw the ray and the ray. After the measurement, it can be verified that is a right angle. Hence the ray and the ray are perpendicular to each other.