Question

Draw a right angle and construct its bisector.

Answer 1

Draw the right angle with its bisector.

The processes for constructing a right angle and its bisector are outlined below:

1. Make a line $L$ with a point $A$ on it. Consider point $A$ as the center of an arc with a convenient radius. Allow this to cross line $L$ at $B$.
2. Consider $B$ as the center and draw an arc with the same radius as before, intersecting the previously drawn arc at $C$.
3. Using $C$ as the center, draw an arc intersecting the arc at $D$, as shown in the figure, with the same radius as before.
4. Using $C$ and $D$ as centers, draw arcs with the same radius that cross at $G$.
5. Join the $AG$. The needed ray is $D$, which forms a right angle with the line $L$. At point $E$, let this intersect the primary arc.
6. Using $B$ and $E$ as the centers, draw arcs with a radius greater than $\frac{1}{2}BE$ that intersect at point $F$. Join the $PF$.

The is required bisector of the right angle is $PF$ as shown below:

Hence, the diagram of a right angle with its bisector is shown below: