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Classify the Bolded Triangle Segment as an Angle Bisector, Median, Altitude, or Perpendicular Bisector
Mathematics
Grade 10 (High School)
Question Content
Given the diagram, classify the bolded line as a perpendicular bisector, angle bisector, median, or altitude. Write your answer on the line.
Correct Answer
Angle Bisector
Detailed Solution Steps
1
Step 1: Recall the definitions of the triangle segments: An angle bisector is a segment from a vertex that splits the vertex angle into two equal smaller angles, marked by congruent angle symbols in the diagram.
2
Step 2: Observe the diagram: The bolded line connects a vertex and splits the angle at that vertex into two congruent angles (marked by matching angle arcs).
3
Step 3: Match to the definition: This fits the definition of an angle bisector.
Knowledge Points Involved
1
Angle Bisector of a Triangle
An angle bisector is a segment or ray that starts at a triangle's vertex and divides that vertex angle into two congruent (equal-measure) angles. The three angle bisectors of a triangle intersect at the incenter.
2
Triangle Segment Identification
Classifying triangle segments requires comparing their visual properties to formal definitions: angle bisectors split angles, medians connect to midpoints, altitudes are perpendicular to sides, and perpendicular bisectors are perpendicular to sides at their midpoints.
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