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Concurrent Lines, Medians & Altitudes

Concurrent Lines, Medians & Altitudes. Geometry Honors. Vocabulary. Concurrent Lines – when three or more lines intersect in one point. Point of concurrency – the point at which 3 or more lines intersect. Geogebra Demonstration of Perpendicular Bisectors. Vocabulary.

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Concurrent Lines, Medians & Altitudes

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  1. Concurrent Lines, Medians & Altitudes Geometry Honors

  2. Vocabulary Concurrent Lines – when three or more lines intersect in one point. Point of concurrency– the point at which 3 or more lines intersect.

  3. Geogebra Demonstration of Perpendicular Bisectors

  4. Vocabulary Circumcenter of the triangle– the point of concurrency of the perpendicular bisectors. Circumcenter

  5. Theorem The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.

  6. Since the vertices of the triangle are equidistant from the circumcenter, we can draw a circle around the triangle or circumscribe the triangle. The center of the circle is the circumcenter of the triangle.

  7. Geogebra Demonstration of Angle Bisectors

  8. Vocabulary Incenter of the triangle– the point of concurrency of the angle bisectors. Incenter

  9. Theorem The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides.

  10. We can now inscribe a circle in the triangle since the incenter is equidistant from the sides. The center of the circle is the incenter of the triangle.

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