Concurrent Lines, Medians amp Altitudes CunninghamWAHS …并行线，中线amp；海拔cunninghamwahs—….pptVIP

Example: A(6,9) B(-2,3) C(12,-1) How can we find the slope of the perpendicular bisector of BC? D Since we know that perpendicular bisectors form right angles, we can determine the slope of BC and then use opposite reciprocals to determine the slope of the perpendicular bisector of BC. CONCURRENT LINES, MEDIANS ALTITUDES 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 Circumcenter of the triangle– the point of concurrency of the perpendicular bisectors. Circumcenter The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Theorem 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. Geogebra Demonstration of Angle Bisectors Vocabulary Incenter of the triangle– the point of concurrency of the angle bisectors. Incenter Theorem The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. 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. Geogebra Demonstration of Altitudes of Triangles Vocabulary Altitude of a Triangle– a perpendicular segment from a vertex to the line containing the side opposite to the vertex. Orthocenter FYI An altitude can be the side of the triangle. Theorem The lines that contain the altitudes of a triangle are concurrent. Geogebra Demonstration of Medians of Triangles Vocabulary Median of a Triangle– a segment whose endpoints are a vertex and the midpoint of the opposite side. Centroid FYI The centroid is the center of gravity of the triangle. If you cut out t