Chapter 3 Vocabulary - Discovering Geometry

Segment bisector

• The three medians of a triangle are concurrent
• A line, ray, or segment that passes through the midpoint of a segment
• Balance point
• The segment connecting the vertex of a triangle to the midpoint of its opposite side

Perpendicular bisector

• The three medians of a triangle are concurrent
• The three perpendicular bisectors of a triangle are concurrent
• The centroid of a triangle is the center of gravity of the triangular region
• A line or segment that divides a line segment into two equal parts and also makes a right angle with that line segment.

Perpendicular Bisector Conjecture

• Balance point
• The length of the perpendicular segment from the point to the line
• The point on the line segment that is the same distance from both endpoints
• If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints

Converse of the Perpendicular Bisector Conjecture

• The centroid of a triangle is the center of gravity of the triangular region
• The point of concurrency for the perpendicular bisectors
• If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
• A line or segment that divides a line segment into two equal parts and also makes a right angle with that line segment.

Median

• The segment connecting the vertex of a triangle to the midpoint of its opposite side
• The point of concurrency for the three altitudes
• The point of concurrency for the perpendicular bisectors
• The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line

Midsegment

• 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
• The segment connecting the vertex of a triangle to the midpoint of its opposite side
• The center of a circle that circumscribes the triangle; therefore, called the circumcenter of the triangle
• The segment that connects the midpoints of two sides of a triangle

Shortest Distance Conjecture

• The segment connecting the vertex of a triangle to the midpoint of its opposite side
• 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
• The three angle bisectors of a triangle are concurrent (meet at a point)
• The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line

Distance from a point to a line

• The three angle bisectors of a triangle are concurrent (meet at a point)
• The point of concurrency of the three medians
• The three medians of a triangle are concurrent
• The length of the perpendicular segment from the point to the line

Altitude (of a triangle)

• A perpendicular segment from a vertex to the opposite side or to a line containing the opposite side
• If two lines are cut by a transversal to form congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel
• The three perpendicular bisectors of a triangle are concurrent
• The point of concurrency of the three medians

Angle Bisector Conjecture

• The point of concurrency for the perpendicular bisectors
• If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
• Touches each side of the polygon at exactly one point
• The segment connecting the vertex of a triangle to the midpoint of its opposite side