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# Discovering Geometry Chapter 3 Conjectures

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Perpendicular Bisector Conjecture
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. (Lesson 3.2) Circumcenter
Converse of the Perpendicular Bisector Conjecture
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. (Lesson 3.2)
Shortest Distance Conjecture
The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line. (Lesson 3.3)
Angle Bisector Conjecture
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. (Lesson 3.4) Incenter
Angle Bisector Concurrency Conjecture
The three angle bisectors of a triangle are concurrent (meet at a point). (Lesson 3.7)
Perpendicular Bisector Concurrency Conjecture
The three perpendicular bisectors of a triangle are concurrent. (Lesson 3.7)
Altitude Concurrency Conjecture
The three altitudes (or the lines containing the altitudes) of a triangle are concurrent. (Lesson 3.7)
Circumcenter Conjecture
The circumcenter of a triangle is equidistant from the vertices. (Lesson 3.7)
Incenter Conjecture
The incenter of a triangle is equidistant from the sides. (Lesson 3.7)
Median Concurrency Conjecture
The three medians of a triangle are concurrent.
(Lesson 3.8)
Centroid Conjecture
The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side. (Lesson 3.8)
Center of Gravity Conjecture
The centroid of a triangle is the center of gravity of the triangular region. (Lesson 3.8)