Math Problem Statement
Solution
In this question, we are tasked with identifying which segment is an angle bisector of .
Step-by-step solution:
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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.
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Analyze the Diagram:
- In the given triangle , several line segments are drawn, such as , , , and .
- The angle bisector should start at one vertex (e.g., , , or ) and split the corresponding angle into two congruent angles.
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Observation: The segment starts at and divides into two equal parts, as shown by the arc markings in the diagram. Hence, is the angle bisector of .
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Answer: The correct option is: D.
Would you like further clarification or additional details?
Related Questions:
- What is the significance of an angle bisector in a triangle?
- How can you mathematically prove that a segment is an angle bisector?
- What is the relationship between angle bisectors and the incenter of a triangle?
- How does the angle bisector theorem help in solving geometric problems?
- 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
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