Math Problem Statement

Which segment is an angle bisector of △ABC?

Solution

In this question, we are tasked with identifying which segment is an angle bisector of ABC\triangle ABC.

Step-by-step solution:

  1. Definition of an Angle Bisector: An angle bisector divides an angle into two equal parts. In a triangle, an angle bisector connects a vertex of the triangle to the opposite side, creating two smaller angles that are congruent.

  2. Analyze the Diagram:

    • In the given triangle ABC\triangle ABC, several line segments are drawn, such as BWBW, RZRZ, ASAS, and SXSX.
    • The angle bisector should start at one vertex (e.g., AA, BB, or CC) and split the corresponding angle into two congruent angles.
  3. Observation: The segment SXSX starts at AA and divides BAC\angle BAC into two equal parts, as shown by the arc markings in the diagram. Hence, SXSX is the angle bisector of ABC\triangle ABC.

  4. Answer: The correct option is: D. SXSX


Would you like further clarification or additional details?

Related Questions:

  1. What is the significance of an angle bisector in a triangle?
  2. How can you mathematically prove that a segment is an angle bisector?
  3. What is the relationship between angle bisectors and the incenter of a triangle?
  4. How does the angle bisector theorem help in solving geometric problems?
  5. How do you construct an angle bisector using a compass and straightedge?

Tip:

Always look for congruency markers (like arcs or tick marks) in diagrams to identify angle bisectors or other special segments.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Bisectors

Formulas

Angle bisector divides an angle into two congruent angles

Theorems

Angle Bisector Theorem

Suitable Grade Level

Grades 6-8