# 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)

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