Honors Geometry - Chapter 5

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Perpendicular Bisector
Goes through midpoint and is perpendicular to a side.
Circumcenter
The point of intersection of the perpendicular bisectors.
Circumcenter Theorem
This point of a triangle is equidistant from the vertices of the triangle.
Median
Starts at the midpoint and goes to a vertex.
Centroid
The point of intersection of the medians.
Centroid Theorem
The special point involved with this theorem is located 2/3 of the distance from a vertex to the midpoint of the side opposite the vertex on a median.
Altitude
Starts at a vertex and goes perpendicular to a side.
Orthocenter
The point of intersection of the altitudes.
Angle Bisector
A segment that cuts an angle in half equally.
Incenter
The point of intersection of the angle bisectors.
Incenter Theorem
The special point involved with this theorem is equidistant from each side of the triangle.
Exterior Angle Theorem
If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles.
Opposite Angle Theorem
If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
Opposite Side Theorem
The bigger angle is opposite the longer side and the smaller angle is opposite the smaller side.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
SAS Inequality / Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, then the bigger included angle is opposite the longer side and the smaller included angle is opposite the shorter side.
SSS Inequality Theorem
If two sides of one triangle are congruent to two sides of another triangle, then the third side that is longer is opposite the bigger angle and the third side that is shorter is opposite the smaller angle.
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