Midsegments and Perpendicular/Angle Bisectors

The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

A midsegment in a triangle is a segment that connects the midpoints of two sides of the triangle.

The length of a midsegment is half the length of the third side of the triangle.

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

If point C lies on the perpendicular bisector of segment AB, then AC = BC.

A midsegment is parallel to one side of the triangle and its length is half the length of that side.

The converse of the Perpendicular Bisector Theorem states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of that segment.

An angle bisector is a ray that divides an angle into two equal angles.

To determine if a point is on the perpendicular bisector of a segment, check if it is equidistant from the endpoints of the segment.