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Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side that is half as long as that side.
Perpendicular Bisector Theorem
In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Theorem
In a plane, if a point is equidistant from the endpoints of a segment, then it is on perpendicular bisector of the segment.
Concurrency of Perpendicular Bisectors of a Triangle
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the triangle
Converse of the Angle Bisector Theorem
If a point is in the interior of an angle and is equidistant from the sides of the triangle, then it lies on the midpoint of the angle.
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non adjacent, interior angles.
Triangle Inequality Theorem
The sum of the lengths of any two given sides is larger than the other side.
Concurrency of Altitudes of a Triangle
The lines containing the altitudes of the triangle are congruent.
Midsegment of the Triangle
segment that connects the midpoints of the two sides of a triangle is parallel to the third side and is half as long as that side
Coordinate Proof
placing geometric figures on a plane.
Perpendicular Bisector
A segment or Ray the perpendicularly bisects a side of a 🔺
Equidistant
If a point is on the angle bisector, the distance from the two sides of the angle
Concurrent
Three or more lines that intersect at the same point
Point of Concurrency
where 3 lines meet
Incenter
The point where three angle bisectors of a triangle intersect
Median of Triangles
Segment from vertex to midpoint
centroid
The point where three medians of a triangle intersect
altitude of a triangle
perpendicular segment from vertex to the opposite side
Orthocenter
The point where the three altitudes of a triangle intersect