Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4.

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Presentation transcript:

Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4

3 or more lines Concurrent Lines Point of Concurrency intersect at a common point

Angle Bisector Incenter

passes through the midpoint circumcenter Perpendicular Bisector perpendicular

midpoint centroid Median vertex

Altitude perpendicular orthocenter

Special Segment altitude angle bisector median perpendicular bisector Characteristics vertexmidpoint  separates an angle in half

Example: bisectsEDF,F = 80, and E = 30, find DGE. If

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.

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. THEOREM

Example: Points X, Y, and Z are midpoints. Find a, b, and c.