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5.15.2 HW worksheet odds 1 November 05, 2013 Nov 88:13 AM 5.1 Midsegment of a T Midsegment of a Triangle: segment that connects the midpoints of 2 side Every triangle has 3 midsegments. Midsegement Theorem: midsegment is parallel to the 3 side and is 1/2 as A C B E D F DE // AC DE = 1/2 AC DF // BC DF = 1/2 BC EF // BA EF = 1/2 BA

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Midsegements & Perpendicular Bisectors

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5.1 Midsegment of a TriangleMidsegment of a Triangle: segment that connects the midpoints of 2 sides of a triangle 

Every triangle has 3 midsegments.

Midsegement Theorem: midsegment is parallel to the 3 side and is 1/2 as long

A C

B

ED

F

DE // ACDE = 1/2 AC

DF // BCDF = 1/2 BC

EF // BAEF = 1/2 BA

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5.2 Perpendicular BisectorsEquidistant: same distancePerpendicular Bisector: a segment that is perpendicular to a segment at its midpoint.

CP is   bisesctor of ABA BCP

A B

C

PIf CP is      bisesctor of AB, then CA = CB

A BCP

D

If DA = DB, then D lies on the   bisesctor of AB.

Perpendicular Bisector Theorem: If a point is on the    bisector, then it is equidistant from the endpoints of the segment. 

Converse of the Perpendicular Bisector Theorem: If a point in equidistant from the endpoints of a segment, then it is on the    bisector.

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Concurrent: when 3 or more lines intersect in the same pointPoint of Concurrency: the point of intersection

Circumcenter: the point of concurrency of the 3 perpendicular bisectors of a triangle

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Concurrency of Perpendicular Bisector Theorem: the perpendicular bisector of a triangle intersects at a point that is equidistant from the vertices.

A

B

C

P

AP=BP=CP

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