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Perpendicular Bisectors, Angle Bisectors, Medians, & Altitudes

Perpendicular Bisectors, Angle Bisectors, Medians, & Altitudes. Section 5-2 & 5-4. Perpendicular Bisector. A perpendicular bisector of a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint. Perpendicular Bisector Theorems.

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Perpendicular Bisectors, Angle Bisectors, Medians, & Altitudes

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  1. Perpendicular Bisectors, Angle Bisectors, Medians, & Altitudes Section 5-2 & 5-4

  2. Perpendicular Bisector • A perpendicular bisectorof a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint.

  3. Perpendicular Bisector Theorems • Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. • Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of a segment.

  4. Perpendicular Bisector Theorems

  5. Theorems about Angle Bisectors • Angle Bisector Theorem: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. • Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

  6. Theorems about Angle Bisectors

  7. Median • A median of a triangle is a segment from a vertex to the midpoint of the opposite side. • The three medians of a triangle meet at a point, called the centroidof the triangle.

  8. Altitude • An altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side. • Acute triangles: the three altitudes are all inside the triangle • Right triangles: two of the altitudes are the legs of the triangles • Obtuse triangles: two of the altitudes are outside of the triangle.

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