Special segments in a triangle

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5.2

• Special segments in a triangle

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IDENTIFYING SPECIAL SEGMENTS
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PERPENDICULAR BISECTOR

• A SEGMENT THAT IS PART OF A BISECTOR OF ONE
  OF THE SIDES.

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ANGLE BISECTOR

• A SEGMENT THAT BISECTS 1 OF THE ANGLES OF A
  TRIANGLE

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MEDIAN

• SEGMENT WHOSE ENDPOINTS ARE A VERTEX AND THE
  MIDPOINT OF THE OPPOSITE SIDE

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ALTITUDE

• A SEGMENT FROM A VERTEX THAT IS TO THE
  OPPOSITE SIDE . MAY LIE INSIDE OR OUTSIDE THE

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CONCURRENCY PROPERTIES

• THESE PROPERTIES ARE BASED ON THE FACT THAT EVERY
  HAS 3 BISECTORS, 3 ANGLE BISECTORS, 3
  MEDIANS AND 3 ALTITUDES.

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CONCURRENT

• EACH SET OF SPECIAL SEGMENTS INTERSECTS AT ONE
  POINT

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CIRCUMCENTER

• THE COMMON POINT FOR THE BISECTORS
• THE CIRCUMCENTER IS EQUIDISTANT FROM THE VERTICES

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CIRCUMCENTER

• THE CENTER OF THE CIRCUMSCRIBED CIRCLE THAT
  PASSES THROUGH THE VERTICES OF THE TRIANGLE.

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CIRCUMCENTER
B

• AC BC DC

C
A
D
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INCENTER

• THE COMMON POINT OF THE lt BISECTORS.
• THE INCENTER IS EQUIDISTANT FROM THE 3 SIDES OF
  THE TRIANGLE.

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INCENTER

• THE CENTER OF THE INSCRIBED CIRCLE OF THE
  TRIANGLE.

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INCENTER

• SE SF SD

B
D
F
S
A
C
E
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CENTROID

• THE COMMON POINT OF THE MEDIANS.
• THE CENTROID IS 2/3 OF THE DISTANCE FROM EACH
  VERTEX TO THE MIDPOINT OF THE OPPOSITE SIDE

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CENTROID

• PC 2/3(CF)

B
D
F
P
A
C
E
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ORTHOCENTER

• THE COMMON POINT OF THE ALTITUDES.