Maths 5.1 & 5.2 Therums

Honors Geo

What does the Perpendicular Bisector Theorem say?

If a point is on the perpendicular bisector of a segment, it’s the same distance from both ends of the segment.

What does the Converse of the Perpendicular Bisector Theorem say?

If a point is the same distance from both ends of a segment, then it’s on the perpendicular bisector.

What does the Circumcenter Theorem say?

The perpendicular bisectors of a triangle meet at the circumcenter, which is the same distance from all corners (vertices) of the triangle.

What does the Angle Bisector Theorem say?

If a point is on an angle bisector, it’s the same distance from both sides of the angle.

What does the Converse of the Angle Bisector Theorem say?

If a point is the same distance from both sides of an angle, then it’s on the angle bisector.

What does the Incenter Theorem say?

The angle bisectors of a triangle meet at the incenter, which is the same distance from all sides of the triangle.

What does the Centroid Theorem say?

The medians of a triangle meet at the centroid, which is 2/3 of the way from each vertex to the midpoint of the opposite side.

What is the Orthocenter Theorem (Key Concept)?

The altitudes of a triangle meet at one point called the orthocenter.