splitting Angles

Angles deserve to be divided similar to ordinary numbers. An angle can only be separated by a ray on the interior of the angle, though. Together a beam that divides an angle right into two equal angle is called an edge bisector. Likewise, two rays that divide an angle into three congruent angles are dubbed angle trisectors.

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

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Figure %: An edge bisected and also trisectedOn the left, angle alphabet is bisected through the ray BD. To understand this, we must know that angle ABD and also angle CBD space congruent. On the right, angle abc is trisected by beam BE and also ray BF. In this case, the 3 angles ABE, EBF, and FBC room congruent.

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

separating Segments

A segment is divided into 2 equal segments only when a line or segment passes through the midpoint of the original segment. The midpoint the a segment is the allude lying in the segment that is exactly halfway from each endpoint the the segment.

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

Bisectors

When a line or segment passes v the midpoint of an additional segment, that line or segment is a bisector that the various other segment. There are an infinite number of bisectors for every segment, relying on the angle at i beg your pardon the incoming segment or line bisects the various other segment.

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Figure %: A segment gift bisected by numerous different lines and segmentsThe segment AB, v midpoint M, is bisected by segment CD, heat EF, and also segment GH.

Perpendicular Bisectors

If a bisector is perpendicular come the segment the bisects, that is called the perpendicular bisector of that segment. Because there exists just one line perpendicular come a heat at a provided point, a segment has actually only one perpendicular bisector: the perpendicular line the passes with the midpoint that the segment.

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

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Just together there space bisectors for segments, there space trisectors, too.Segment trisectors division a segment into three equal segments.