Question

Which diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?
(a)

(b)

(c)

(d) None of these

Answer 1

Hint: In this given problem, we are to find the diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle. This requires an arc which can be intersected and also an intersection point drawn by a compass. So, we will try to find those things from an option and if we find it, that is our right option.

Complete step-by-step solution:
According to the problem, we are to find the diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle.
So, we will have to choose the answer from the given options and get the right solution.
To start with, we have the first option as,

Here we can easily see that an angle is given and a line going through the point of the angle is also shown which is again, joining an intersection point.
But, now, to find the bisection of an angle, we need to draw an arc from the vertex which is intersecting all two sides. Now, the arc is missing from both sides of the angle. Then, this is the wrong option.
Again, for the second option, we have,

Similarly, if we state the point of the first option, that, to find the bisection of an angle, we need to draw an arc from the vertex which is intersecting all two sides. But from the given image we can see that there is no arc given in the image we have. And also with that there is no intersection point where we can find the use of compass here. So, this is also the wrong option.
Our third option gives us,

Now, in this option, we get, an arc is drawn touching both sides of the angle, and along with that an intersection point is also given to get the bisector of the given angle. So, this is the correct option.

Note: To bisect an angle, we need to draw an arc from the vertex which intersects all the two sides. Then draw an arc from the point where the first arc(from vertex) intersects the lines. Draw a line by joining the vertex of an angle and the point of intersection of two arcs. The new line formed will bisect the angle.