Video: Recognizing the Construction of an Angle Bisector

What does the following figure illustrate? [A] a bisector of an angle. [B] an angle congruent to another angle. [C] a perpendicular from a point lying outside a straight line. [D] a straight line parallel to another line. [E] a bisector of a line segment.

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Video Transcript

What does the following figure illustrate? Is it A) a bisector of an angle, B) an angle congruent to another angle, C) a perpendicular from a point lying outside a straight line, D) a straight line parallel to another line, or E) a bisector of a line segment.

As our two lines 𝐴𝐵 and 𝐵𝐶 are neither perpendicular nor parallel, we can immediately rule out options C, D, and E. Once there are two congruent or equal angles 𝐴𝐵𝐷 and 𝐷𝐵𝐶, the figure illustrates the bisector of the angle 𝐴𝐵𝐶. This can be drawn using a pair of compasses.

We place our compass point at point 𝐵 and draw the arc from 𝑃 to 𝑄. We then place our compass point at point 𝑃 and draw an arc. We place our compass point at point 𝑄 and draw an equal-length arc. The point at which these two arcs intersect is point 𝑅. Drawing a straight line from 𝐵 to 𝑅 bisects the angle 𝐴𝐵𝐶.

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