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Geometry: Theorems

Terms

Assorted Theorems

Basic Theorems for Triangles

Centroid  -  The point in a triangle at which the medians of a triangle intersect.
Circumcenter  -  The point at which the perpendicular bisectors of a triangle intersect.
Concurrent  -  Intersecting at one point; lines, rays, segments, etc. are concurrent when they intersect at one point.
External Segment  -  The segment contained by a secant segment with an endpoint on the circle and at the fixed point outside the circle whose points all lie outside the circle (except the endpoint on the circle).
Incircle  -  The point in a triangle at which the angle bisectors of a triangle intersect. This point is also the center of a circle inscribed in the triangle.
Inscribed Angle  -  An angle whose vertex lies on a circle and whose sides are contained by secant lines.
Internal Segment  -  The segment contained by a secant segment whose endpoints are both on the circle.
Isosceles Trapezoid  -  A trapezoid with congruent legs.
Lower Base Angles  -  The angles in an isosceles trapezoid whose vertices are the endpoints of the longer base.
Median of a Triangle  -  A segment within a triangle with one endpoint at a vertex of the triangle and the other endpoint at the midpoint of the side opposite the vertex. Every triangle has three medians.
Midsegment  -  A segment within a triangle whose endpoints are midpoints of the sides of the triangle. Every triangle has three midsegments.
Orthocenter  -  The point at which the altitudes of a triangle intersect.
Point of Concurrency  -  The intersection point of concurrent lines, segments, etc.
Remote Interior Angles  -  The two angles of a triangle that are not adjacent to the exterior angle which is drawn by extending one of the sides.
Secant Segment  -  A segment with one endpoint on a circle, the other endpoint at a fixed point outside the circle, and one point of intersection with the circle, not including its endpoint.
Theorem  -  A statement about geometric figures that has been proved in the past, and can be accepted as a truth in the present without proof. A list of important theorem's can be found in review.
Upper Base Angles  -  The two angles of an isosceles trapezoid whose vertices are the endpoints of the smaller base.

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