Points of Concurrency in Points of Concurrency in TrianglesTriangles

MM1G3.eMM1G3.e

Point of concurrencyPoint of concurrency - the - the place where three or more place where three or more lines, rays, or segments lines, rays, or segments

intersect at the same intersect at the same pointpoint

Angle bisectorAngle bisector – a line or – a line or ray that divides an angle ray that divides an angle

in halfin half

incenterincenter – the point of – the point of concurrency of the three concurrency of the three

angle bisectors of a angle bisectors of a triangletriangle

altitudealtitude – the – the perpendicularperpendicular segment segment from one from one vertexvertex of the of the

triangle to the opposite triangle to the opposite side or to the line that side or to the line that

contains the opposite sidecontains the opposite side

orthocenterorthocenter – the point of – the point of concurrency of the three concurrency of the three

altitudes of a trianglealtitudes of a triangle

Perpendicular bisectorPerpendicular bisector – a – a segment, ray, or line that segment, ray, or line that

is is perpendicularperpendicular to a to a segment at its segment at its midpointmidpoint

circumcentercircumcenter – the point – the point of concurrency of the of concurrency of the three perpendicular three perpendicular

bisectors of a trianglebisectors of a triangle

medianmedian – a segment from – a segment from a a vertexvertex of a triangle to of a triangle to

the the midpointmidpoint of the of the opposite sideopposite side

centroidcentroid – the point of – the point of concurrency of the three concurrency of the three

medians of a trianglemedians of a triangle

1. What is the difference between an altitude and a perpendicular bisector?2. Classify

Term Starts from the vertex Doesn’t start from vertex

Angle bisector

Altitude

Perpendicular bisector

Median