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# Geometry, 5.1 - 5.3

### Midsegments, bisectors, and points of concurrency.

A midsegment connects the ___ of 2 sides on a ___. midpoints; triangle
Midsegment theorem- the midsegment of a triangle is parallel to the __ side and __ its length. 3rd; 1/2
Theorem 5.2- If a point is on the perp. bisector of a segment, then it is ____ from the ___ of the segments. equidistant; enpoints
Theorem 5.3- If a point is equidistant from the ___ of a segment, then it is on the ____ ____ of the segment. endpoints; perpendicular bisector
Theorem 5.4- If a point is on the ____ of an ____, then the point is ____ from the sides of the angle. bisector; angle; equidistant
Theorem 5.5- If a point in the ____ of an angle is ____ from the sides of the angle, then the point is on the ____ ____. interior; equidistant; angle bisector
A point on the perp. bisector of a segment is Equidistant to the endpoints
A point on an angle bisector is Equidistant to the sides of the angle
Slope formula Y2 - Y1 over X2 - X1
How to find a midpoint m= (X1+X2 over 2, Y1+Y2 over 2)
Circumcenter is formed by Perpendicular bisectors
A circumcenter is the Center of the circle outside the triangle
Incenter is formed by Angle bisectors
An incenter is the Center of the circle inside the triangle
Centroid is formed by Medians
A centroid is 2/3 (2:1) the distance from vertex to midpoint
Orthocenter is formed by Altitudes
An orthocenter has No mathematical relationship
How to find circumcenter: Midpoint to perpendicular bisector
How to find incenter Vertex to side (does not have to be midpoint)
How to find centroid Vertex to midpoint
How to find orthocenter Vertex to perpendicular side, forming a right angle
Created by: mma129