splitting Angles

Angles deserve to be divided as with ordinary numbers. An angle deserve to only be separated by a ray on the interior of the angle, though. Such a ray that divides one angle into two equal angles is called an edge bisector. Likewise, two rays that division an angle right into three congruent angle are referred to as angle trisectors.

You are watching: A ray that divides an angle into two congruent angles

Figure %: An edge bisected and trisectedOn the left, angle alphabet is bisected by the beam BD. To know this, we must understand that edge ABD and angle CBD space congruent. On the right, angle alphabet is trisected by beam BE and ray BF. In this case, the three angles ABE, EBF, and also FBC space congruent.

With edge bisectors and trisectors, it additionally holds true that any type of of the brand-new angles developed by the bisector or trisector is equal to specifically one-half or one-third that the original angle, depending on whether the angle has actually been bisected or trisected.

dividing Segments

A segment is separated into two equal segment only as soon as a heat or segment passes v the midpoint of the initial segment. The midpoint the a segment is the point lying in the segment the is exactly halfway from every endpoint of the segment.

Figure %: The midpoint that a segmentIn the over figure, the segment abdominal is split into 2 segments, AM and MB. Point M is the midpoint of segment AB, thus AM and MB space of the very same length: one-half the length of AB.


When a line or segment passes v the midpoint of another segment, the line or segment is a bisector that the various other segment. There are an infinite variety of bisectors because that every segment, depending on the angle at which the just arrived segment or heat bisects the other segment.

Figure %: A segment being bisected by many different lines and also segmentsThe segment AB, through midpoint M, is bisected by segment CD, heat EF, and also segment GH.

Perpendicular Bisectors

If a bisector is perpendicular come the segment it bisects, it is referred to as the perpendicular bisector of that segment. Due to the fact that there exists just one line perpendicular come a line at a given point, a segment has only one perpendicular bisector: the perpendicular line the passes v the midpoint that the segment.

Figure %: A perpendicular bisectorThe heat CD has the midpoint of segment AB, and also forms a best angle v the segment. Therefore, that is the perpendicular bisector of segment AB.

See more: What Is The Area Of An Equilateral Triangle That Has Sides Of 2 Yards And A Height Of 4.25 Feet?

Just together there room bisectors because that segments, there room trisectors, too.Segment trisectors divide a segment right into three same segments.