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What is the name of the line that divides an angle into two equal parts?
  • a)
    Angle bisector
  • b)
    Perpendicular bisector
  • c)
    Median
  • d)
    Altitude
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the name of the line that divides an angle into two equal part...
An angle bisector is a line or ray that divides an angle into two equal parts, creating two angles of the same measure.
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What is the name of the line that divides an angle into two equal part...
Understanding Angle Bisectors
An angle bisector is a special line segment that plays a crucial role in geometry. Here’s a detailed explanation of why the correct answer is option 'A'.
Definition of an Angle Bisector
- An angle bisector is a line or ray that divides an angle into two equal smaller angles.
- For example, if an angle measures 40 degrees, the angle bisector creates two angles of 20 degrees each.
Characteristics of Angle Bisector
- Equal Division: The primary characteristic is that it splits the angle into two equal parts.
- Interior Point: The point where the angle bisector meets is located inside the angle.
Other Types of Lines (For Clarity)
- Perpendicular Bisector: This line divides a segment into two equal parts at a right angle (90 degrees) but does not relate to angles.
- Median: A median connects a vertex of a triangle to the midpoint of the opposite side, not related to angle division.
- Altitude: An altitude is a perpendicular segment from a vertex to the opposite side, focusing on height rather than angle division.
Importance of Angle Bisectors
- Angle bisectors are significant in various geometric constructions.
- They are used in determining inradii of triangles and can help solve problems involving angles and triangles.
In conclusion, the angle bisector is essential in geometry for its unique property of equally dividing angles, which makes it the correct answer to the question posed.
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