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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