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

We are asked to draw a linear pair of angles and bisect each of them and verify that the two bisecting rays are perpendicular to each other

We follow the following algorithm to construct

$$\Rightarrow$$Steps of construction

STEP $$1$$: Draw a linear pair of angles and label them as $$ABD$$ and $$DBC$$.

STEP $$2$$: Draw an arc of sufficient radius, intersecting the ray $$BA$$, ray $$BD$$ and the ray $$BC$$ at points $$G, H$$ and $$I$$ respectively.

STEP $$3$$: With centre, $$I$$ and radius greater than half of $$HI$$ draw an arc inside of $$DBC$$.

STEP $$4$$: With centre $$G$$ and the same radius draw an arc inside of $$ABD$$.

STEP $$5$$: 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 STEP $$4$$ at $$E$$.

STEP $$6$$: Draw the ray $$BE$$ and the ray $$BF$$.

After the measurement, it can be verified that $$EBF$$ is a right angle.

Hence the ray $$BE$$ and the ray $$BF$$ are perpendicular to each other.