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The longest side in a triangle will be across from the largest angle. The smallest side will be across from the smallest angle.

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The sum of the lengths of any two sides of a triangle must be greater than the 3rd side

a+c > b
a+b > c
c+b > a

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a line perpendicular to one side of a triangle that goes through the opposite vertex

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Concurrent: 3 or more lines that intersect at 1 point. The intersection point is called the center of concurrency.

Median: a segment connecting the midpoint of one side of a triangle with the opposite vertex (corner); point of concurrency splits median into sections where one is 2x as long as the other.
Ex: CP

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Section 5.3- Concurrent Lines, Medians and Altitudes

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Section 5.3- Concurrent Lines, Medians and Altitudes

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Angle Bisector Theorem and it's Converse

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Angle Bisector Theorem and it's Converse

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The Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from both sides of the angle
Ex: Point M is equidistant from  Angle LKJ

Converse: If a point is equidistant from both sides of the angle, then it is the angle bisector
Ex: point M

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The Perpendicular Bisector Theorem and it's Converse

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The Perpendicular Bisector Theorem and it's Converse

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The Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint of the segment.
Ex: B is equidistant from DC

Converse: If a point is equidistant from the endpoints of a segment then it is on a perpendicular bisector.
Ex: Point B

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Chapter 5 Relationships Within Triangles

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Chapter 5 Relationships Within Triangles

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By Caroline Casey

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Midsegment: A segment that connects the midpoints of 2 sides of a triangle
Ex: DE is a midpoint

The Midsegment Theorem: A Midsegment is parallel to and 1/2 the length of the 3rd side of the triangle

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1) https://www.varsitytutors.com/hotmath
2)
https://mathbitsnotebook.com/Geometry/Constructions/centroid1.jpg
3)
http://p5cdn4static.sharpschool.com/UserFiles/Servers/Server_3061305/Image/Lombard/Triangle%20Inequality%20Theorem.png

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A line that cuts an angle into two congruent angles
Ex: M is a angle bisector

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a line that splits a segment into two congruent segments and specifically is perpendicular to the segment
Ex: AB is a perpendicular bisector