GET TUTORING NEAR ME!

A bisector is a line, segment, or plane that divides an angle, line segment, or shape into two equal parts. In geometry, the term bisector is often used to refer to the angle bisector, which is a line or segment that cuts an angle into two congruent angles.

Bisector: Real World Application

1. Construction: Bisector lines are commonly used in construction and engineering to ensure that buildings, bridges, and other structures are properly aligned and symmetrical.
2. Surveying: In land surveying, bisector lines are used to determine the exact location of property boundaries and to ensure that structures are built on the correct parcels of land.
3. Geometry: Bisector lines are used in geometry to find the midpoint of a line segment, the center of a circle, and the angle bisector of a triangle.
4. Robotics: Bisector lines are used in robotics and computer vision to locate and track objects, as well as to navigate and map out environments.
5. Graphics and design: Bisector lines are used in graphics and design to create symmetrical and balanced compositions, as well as to align text and other elements in a layout.
6. Photography: In photography, the rule of thirds is a composition rule that suggest to align a subject with the points of intersection of bisector lines.

Definitions:

• Angle bisector: A line or segment that cuts an angle into two congruent angles.
• Line bisector: A line that divides a line segment into two congruent segments.
• Median: A line segment that connects the midpoint of a side of a triangle to the opposite vertex.
• Altitude: A line segment that connects a vertex of a triangle to the line containing the opposite side, such that it is perpendicular to the line.
• Perpendicular bisector: A line or segment that is perpendicular to and bisects a line segment.

Examples:

1. A line bisector of a line segment is a line that passes through the midpoint of the segment and is parallel to the segment. For example, if the line segment has endpoints A and B, the line bisector would be a line that passes through the midpoint of AB and is parallel to AB.
2. An angle bisector of an angle is a line or segment that cuts the angle into two congruent angles. For example, if angle AOB is bisected by line segment CD, then angle AOC is congruent to angle BOD.
3. A median of a triangle is a line segment that connects the midpoint of a side of a triangle to the opposite vertex. For example, if triangle ABC has a median from vertex A to midpoint D of side BC, the median AD is a line segment connecting vertex A to the midpoint D of side BC.
4. An altitude of a triangle is a line segment that connects a vertex of a triangle to the line containing the opposite side, such that it is perpendicular to the line. For example, if triangle ABC has an altitude from vertex A to line BC, the altitude AE is a line segment connecting vertex A to the line BC, such that it is perpendicular to line BC.
5. A perpendicular bisector of a line segment is a line or segment that is perpendicular to and bisects the line segment. For example, if the line segment has endpoints A and B, the perpendicular bisector would be a line that passes through the midpoint of AB, is perpendicular to AB and bisects the line segment.

10 Question Quiz:

1. What is the definition of an angle bisector?
2. What is the definition of a line bisector?
3. What is the definition of a median?
4. What is the definition of an altitude?
5. What is the definition of a perpendicular bisector?
6. What is the name of the line or segment that cuts an angle into two congruent angles?
7. What is the name of the line that divides a line segment into two congruent segments?
8. What is the name of the line segment that connects the midpoint of a side of a triangle to the opposite vertex?
9. What is the name of the line segment that connects a vertex of a triangle to the line containing the opposite side, such that it is perpendicular to the line?
10. What is the name of the line or segment that is perpendicular to and bisects a line segment?

Answers:

1. Angle bisector
2. Line bisector
3. Median
4. Altitude
5. Perpendicular bisector 6