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# Honors Geometry

### Chapter 5

Coordinate Proof Involves placing a geometric figure in a coordinate plane and utilizing variables to represent the coordinates proofs done in this manner are then true for all figures
Midsegment of a Triangle The segment that connects the midpoint of two sides of the triangle
Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
Perpendicular Bisector A segment, ray, line, or plane that is perpendicular to a segment at its midpoint
Equidistant When a point is the same distance between two figures
Perpendicular Bisector Theorem In a plane if a point is on the perpendicular bisector of a segment then it is equidistant from the end points of the segment.
Converse of the Perpendicular Bisector Theorem In a plane if a point is equidistant from the end of the segment, then it is on the perpendicular bisector of a segment.
Concurrent lines, rays or segments when three or more lines, rays, or segments intersect
Concurrency of the Perpendicular Bisector Theorem The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
Circumcenter The point of concurrency if the three perpendicular bisects of a triangle. The location of the circumcenter depends on the type of circle. Acute- In the triangle Right- On the triangle Obtuse- Outside of the triangle.
Angle Bisector Theorem If a point is on the bisector of an angle, the it is equidistant from the two sides of an angle.
Converse Angle Bisector Theorem If a point is on the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.
Concurrency of the Angle Bisectors of a triangle The angle bisectors of a triangle intersect at a point that is equidistant from the sides of a triangle.
Incenter The point of concurrency of the three angle bisectors of a triangle. Always on the inside of a triangle.
Median of a triangle A segment from a vertex to the midpoint of the opposite side.
Centroid The point of concurrency inside of a triangle. Always located on the median.
Concurrency of the Medians of a triangle The medians of a triangle intersect at a point that is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Altitude of a triangle The perpendicular segment from a vertex to the opposite side or the line that contains the opposite side.
Concurrency of Altitudes of a Triangle The lines containing the altitudes of a triangle are concurrent.
Orthocenter The point at which the lines containing the three altitudes of a triangle intersect.
Triangle Side Length and Angle Relationship The longest side and largest angle are opposite each other. The shortest side and the smallest angle are opposite each other.
Triangle Inequality Theorem The sum of the lengths of any two side of a triangle is greater than the length of the third side.
Hinge Theorem If two sides of one triangle are congruent to two side of another triangle, and the included angle of the first is larger than the included angle of the second than the third side of the first is longer than the third side of the second.
Converse of the Hinge Theorem If two side of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is longer than the included angle of the second.
Indirect Proof A proof in which you prove that a statement is true by first assuming it is false.
Triangle Proportionality Theorem If a line is parallel to one side of a triangle intersects the other two side, then it divides the two sides proportionally.
Converse of the Triangle Proportionality Theorem If a line divided two sides of a triangle proportionally than it is parallel to the third.
Three Parallel lines intersect two transversals Theorem If 3 parallel lines intersect two transversals, then they divide the transversals proportionally.
Ray Bisects Angle of a Triangle Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose length are proportional to the lengths of the other two side.
Created by: smalone27