Question
Bisect a right angle, using ruler and compasses. Measure each part. Bisect each of these parts. What will be the measure of each of these parts?
✓
Answer
Steps of construction are as follows:
Step I: Construct an angle, $\angle\text{ABC}= 90^\circ$
Step II: With $B$ as centre, using compass, draw an arc which cuts both rays of $\angle\text{B}$ at $P$ and $Q.$
Step III: With $P$ as centre, draw $($in the interior of $\angle\text{B})$ an arc, whose radius is more than half of $PQ.$
Step IV: With $Q$ as centre and the same radius, draw another arc in the interior of $\angle\text{B}.$ Let the two arcs intersect at $D.$ Join $BD,$ cutting arc $PQ$ at $L$. Then, $BD$ divides the $\angle\text{ABC}$ into two equal parts.
Step V: Now, taking $P$ and $L$ as centre having radius more than half of $PL,$ draw two arcs respectively, which cut each other at $R.$
Step I: Construct an angle, $\angle\text{ABC}= 90^\circ$
Step II: With $B$ as centre, using compass, draw an arc which cuts both rays of $\angle\text{B}$ at $P$ and $Q.$
Step III: With $P$ as centre, draw $($in the interior of $\angle\text{B})$ an arc, whose radius is more than half of $PQ.$
Step IV: With $Q$ as centre and the same radius, draw another arc in the interior of $\angle\text{B}.$ Let the two arcs intersect at $D.$ Join $BD,$ cutting arc $PQ$ at $L$. Then, $BD$ divides the $\angle\text{ABC}$ into two equal parts.
Step V: Now, taking $P$ and $L$ as centre having radius more than half of $PL,$ draw two arcs respectively, which cut each other at $R.$
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