Midsegements & Perpendicular Bisectors

1. 5.1­5.2
November 05, 2013
5.1
Midsegment of a Triang
Midsegment of a Triangle:
segment that connects the midpoints of 2 sides of a
Every triangle has 3 midsegments.
Midsegement Theorem:
midsegment is parallel to the 3 side and is 1/2 as long
B
D
E
A
F
C
DE // AC
DE = 1/2 AC
DF // BC
DF = 1/2 BC
EF // BA
EF = 1/2 BA
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2. 5.1­5.2
November 05, 2013
Nov 8­11:45 AM
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3. 5.1­5.2
November 05, 2013
Nov 8­11:50 AM
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4. 5.1­5.2
November 05, 2013
5.2
Perpendicular Bisector
Equidistant:
same distance
Perpendicular Bisector:
a segment that is perpendicular to a segment at its midpoint.
C
A
P
B
CP is bisesctor of AB
Perpendicular Bisector Theorem: If a point is on the bisector, then it is equidistant from
the endpoints of the segment.
C
If CP is bisesctor of AB, then CA = CB
A
B
P
Converse of the Perpendicular Bisector Theorem: If a point in equidistant from the
endpoints of a segment, then it is
on the bisector.
C
A
B If DA = DB, then D lies on the bisesctor of AB.
P
D
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5. 5.1­5.2
November 05, 2013
Nov 8­2:02 PM
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6. 5.1­5.2
November 05, 2013
Concurrent:
when 3 or more lines intersect in the same point
Point of Concurrency:
the point of intersection
Circumcenter:
the point of concurrency of the 3 perpendicular bisectors of a
Nov 8­2:01 PM
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7. 5.1­5.2
November 05, 2013
Concurrency of Perpendicular Bisector Theorem: the
perpendicular bisector of a triangle intersects at a point that is
equidistant from the vertices.
B
AP=BP=CP
P
A
C
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8. 5.1­5.2
November 05, 2013
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Nov 8­2:15 PM
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9. 5.1­5.2
November 05, 2013
Nov 15­8:00 AM
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10. 5.1­5.2
November 05, 2013
Nov 15­8:00 AM
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10