Question
Bisect a straight angle, using ruler and compasses. Measure each part.
✓
Answer
Steps of construction are as follows:
Step I: Draw an angle $\angle\text{ABC}=180^\circ.$
Step II: With $S$ as a centre and using compass, draw an arc which cuts both rays of $\angle\text{B.}$ Label point of intersection as $P$ and $Q$.
Step III: With $P$ as centre, draw an arc whose radius is more than half the length $PQ.$
Step IV: With $Q$ as centre and the same radius draw another arc. Let the two arcs intersect at $D.$
Then, $BD$ is the required bisector of $\angle\text{B.}$
Thus, the required angles are $\angle\text{ABD}$ and $\angle\text{CBD.}$
On measuring, $\angle\text{ABD}=\angle\text{CBD}=90^\circ$
Step I: Draw an angle $\angle\text{ABC}=180^\circ.$
Step II: With $S$ as a centre and using compass, draw an arc which cuts both rays of $\angle\text{B.}$ Label point of intersection as $P$ and $Q$.
Step III: With $P$ as centre, draw an arc whose radius is more than half the length $PQ.$
Step IV: With $Q$ as centre and the same radius draw another arc. Let the two arcs intersect at $D.$
Then, $BD$ is the required bisector of $\angle\text{B.}$
Thus, the required angles are $\angle\text{ABD}$ and $\angle\text{CBD.}$
On measuring, $\angle\text{ABD}=\angle\text{CBD}=90^\circ$
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