# Question Video: Determining the Tools Required to Construct an Angle Bisector without a Protractor Mathematics

True or False: Using only a straightedge, you can construct an angle bisector.

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### Video Transcript

True or False: Using only a straightedge, you can construct an angle bisector.

To determine whether this statement is true, weβll need to review the steps required to construct an angle bisector. Letβs sketch ray π΄π΅ and ray π΄πΆ to form an arbitrary angle π΅π΄πΆ. We recall that our very first step requires tracing a circle centered at π΄ that intersects the sides of the angle at two distinct points.

Now, we canβt construct a circle using just a straightedge. It will require a compass. We place the point of our compass on the vertex π΄. Now, we donβt have to trace the whole circle, just an arc that intersects ray π΄π΅ at point π· and ray π΄πΆ at point πΈ. The next step also requires a compass in order to trace two circles of the same radius centered at π· and πΈ. These circles will intersect at a point that we name point πΉ.

It is only in the final step that we use our straightedge to sketch the line π΄πΉ that bisects angle π΅π΄πΆ. As we have demonstrated, we can use a straightedge to construct an angle bisector, but not only a straightedge. Without a compass, we cannot complete the construction. Thus, the given statement is false.

We note that we could alternatively bisect an angle using only a ruler by constructing an isosceles triangle. We would have to measure the sides then connect the midpoint of the base to the opposite vertex.