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Special Segments of Triangles. Advanced Geometry Triangle Congruence Lesson 4. Concurrent Lines. 3 or more lines. intersect at a common point. Point of Concurrency. Angle Bisector. Incenter. Perpendicular Bisector. passes through the midpoint. perpendicular. circumcenter. Median.
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Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4
Concurrent Lines 3 or more lines intersect at a common point Point of Concurrency
Angle Bisector Incenter
Perpendicular Bisector passes through the midpoint perpendicular circumcenter
Median vertex midpoint centroid
Altitude vertex perpendicular orthocenter
Characteristics separates an angle in half Special Segment vertex midpoint altitude angle bisector median perpendicular bisector
Example: If bisects EDF, F = 80, and E = 30, find DGE.
Example: is a perpendicular bisector. If LM = x + 7 and MN = 3x – 11, find the value of x and LN.
Example: is a median, RV = 4x + 9, and VT = 7x – 6. Find the value of x and RV.
THEOREM The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.
Example: Points X, Y, and Z are midpoints. Find a, b, and c.