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Next, keeping the compass set, place its sharp end at the point where one ray intersects the arc. Draw a new arc.
Do the same with the other ray, making sure this arc intersects the previous arc.
Use a ruler or a straightedge to draw a ray from the vertex through the intersection between the two arcs.
This ray is the angle bisector to ∠ D, and divides the angle into two angles of equal measure.
We can prove that EF≅ CF if we show that △ DEF≅ △ DFC. From the diagram, we see that the triangles have two pairs of congruent angles. We also notice that the triangles share DF as a side, which means it is congruent by the Reflexive Property of Congruence.
Now we can claim that △ DEF≅ △ DFC by the AAS (Angle-Angle-Side) Congruence Theorem. Since EF and CF are corresponding sides we know that they are congruent, which means F is equidistant from the sides of ∠ CDE. Therefore, F has to be on the angle bisector according to the Converse of the Angle Bisector Theorem.