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Math
Geometry
Discovering Geometry // Chapter 3
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Terms in this set (27)
Segment bisector
A line, ray, or segment that passes through the midpoint of a segment
Perpendicular bisector
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
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints
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
Median
The segment connecting the vertex of a triangle to the midpoint of its opposite side
Midsegment
The segment that connects the midpoints of two sides of a triangle
Shortest Distance Conjecture
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 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
Angle Bisector Conjecture
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
Converse of the Parallel Lines Conjecture
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
Angle Bisector Concurrency Conjecture
The three angle bisectors of a triangle are concurrent (meet at a point)
Perpendicular Bisector Concurrency Conjecture
The three perpendicular bisectors of a triangle are concurrent
Altitude Concurrency Conjecture
The three altitudes (or the lines containing the altitudes) of a triangle are concurrent
Incenter
The point of concurrency for the three angle bisectors
Circumcenter
The point of concurrency for the perpendicular bisectors
Orthocenter
The point of concurrency for the three altitudes
Circumcenter Conjecture
The circumcenter of a triangle is equidistant from the vertices
Incenter Conjecture
The incenter of a triangle is equidistant from the sides
Point of concurrency of the perpendicular bisectors
The center of a circle that circumscribes the triangle; therefore, called the circumcenter of the triangle
Circumscribed circle
Passes through each vertex of the polygon
Inscribed circle
Touches each side of the polygon at exactly one point
Median Concurrency Conjecture
The three medians of a triangle are concurrent
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
Center of Gravity Conjecture
The centroid of a triangle is the center of gravity of the triangular region
Centroid
The point of concurrency of the three medians
Center of gravity
Balance point
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