Geometry

Question Analysis

This question focuses on identifying the type of special segments in the triangle shown in the diagram, testing knowledge of different line segments related to triangles.

Key Concept Explanation

Altitudes: Perpendicular line segments from a vertex to the opposite side (or its extension). They are used to find the height of a triangle.

Perpendicular Bisectors: Line segments that are perpendicular to a side of a triangle and bisect it. Their intersection gives the circumcenter of the triangle.

Medians: Line segments that connect a vertex of a triangle to the mid - point of the opposite side. Their intersection is the centroid of the triangle.

Angle Bisectors: Line segments that divide an angle of a triangle into two equal - measure angles. Their intersection gives the incenter of the triangle.

Step - by - Step Solution

1. Observe the red arcs in the diagram. These arcs are used to indicate that the angles at each vertex are being divided into equal parts.

2. Recall that the line segments which divide the angles of a triangle into two equal - measure angles are angle bisectors.

Option Analysis

A.Altitudes: Incorrect. Altitudes are perpendicular to the sides and not indicated by the arcs in the diagram.

B.Perpendicular Bisectors: Incorrect. Perpendicular bisectors are perpendicular to and bisect the sides, not related to the angle - dividing arcs shown.

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