### Video Transcript

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

To determine whether this statement
is true, weβll need to review the steps required to construct an angle bisector. Letβs sketch ray π΄π΅ and ray π΄πΆ
to form an arbitrary angle π΅π΄πΆ. 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 canβt 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 donβt have to trace the
whole circle, just an arc that intersects ray π΄π΅ at point π· and ray π΄πΆ at point
πΈ. The next step also requires a
compass in order to trace two circles of the same radius centered at π· and πΈ. These circles will intersect at a
point that we name point πΉ.

It is only in the final step that
we use our straightedge to sketch the line π΄πΉ that bisects angle π΅π΄πΆ. 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.