Concurrent lines
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CONCURRENT LINES PowerPoint PPT Presentation


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CONCURRENT LINES. Three or more lines that intersect at a common point. POINT OF CONCURRENCY. The point at which 3 or more lines intersect. Point of concurrency. CIRCUMCENTER. Point of concurrency for the perpendicular bisectors of a triangle. circumcenter. Circumscribed circle.

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CONCURRENT LINES

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CONCURRENTLINES


Three or more lines that intersect at a common point


POINTOFCONCURRENCY


The point at which 3 or more lines intersect


Point of concurrency


CIRCUMCENTER


Point of concurrency for the perpendicular bisectors of a triangle


circumcenter


Circumscribed circle


A circle that is drawn around a triangle so that each vertex of the triangle is a point on the circle


Circumcenter Theorem

The circumcenter of a triangle is located equidistant from each vertex of the triangle.

BO=AO=CO


INCENTER


Point of concurrency for the angle bisectors of a triangle


incenter

50

50


Inscribed circle


A circle using the incenter of a triangle as its center, and is drawn so that each side of the triangle touches the circle in one point


Incenter Theorem

  • The incenter of a triangle is equidistant from each side of the triangle.

AI = BI = CI

A

I

B

C


MEDIAN


A segment drawn from the vertex to the midpoint of the opposite side of a triangle


4

4


CENTROID


The point where the medians of a triangle intersect


centroid


ALTITUDE


A segment drawn from the vertex of a triangle perpendicular to the opposite side


ORTHOCENTER


Point of concurrency for the altitiudes of a triangle


orthocenter


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