Relationships in Triangles

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Chapter 5

• Relationships in Triangles

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• 5.1 Bisectors, Medians, and Altitudes

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Special Segments in ?s
1. perpendicular bisector line, seg, or ray
that passes thru midpt of side is perpendicular
to it
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Thm 5.1 any pt on perpendicular bisector of a
seg is equidist from endpts of seg
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Thm 5.2 any pt equidist from endpts of seg lies
on perpendicular bis of seg (conv of Thm 5.1)
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Concurrent Lines when 3 or more lines n _at_ a
common pt

• Circumcenter more specialized name of pt of
  concurrency formed by perpendicular biss

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Circumcenter Thm circumcenter of ? is equidist
from vertices of ?
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2. lt bisector line, seg, or ray ing an lt into
2 congruent lts

• Thm 5.4 any pt on lt bis is equidist from the
  sides of lt

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• Thm 5.5 any pt equidist from sides of lt lies on
  lt bis of the lt

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Incenter specialized name for pt of concurrency
formed by lt biss
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3. Median seg whose endpts are vertex midpt
of opp side
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• Centroid specialized name for pt of concurrency
  formed by medians
• Centroid Thm centroid of ? is 2/3 of dist from
  a vertex to midpt of side opp

A
F
B
T
C
E
D
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Ex Points U, V, and W are the midpoints of
respectively. Find a, b, and c.
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4. Altitude (alt) seg from vertex perpendicular
to side opp
Orthocenter - specialized name for pt of
concurrency formed by alts
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Ex MS is alt, lt13x11, lt27x9. Find x lt2
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2
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Summary

• Special seg
• Perpendicular bis
• lt bis
• Median
• Alt

• Pt of concurrency
• Circumcenter
• Incenter
• Centroid
• Orthocenter

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• 5.1 worksheet