Midsegments and Perpendicular/Angle Bisectors

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and half its length.

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

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

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the lengths of the two sides of the triangle that form the angle.

To find the length of a midsegment, measure the lengths of the two sides it connects, and then use the formula: Length of midsegment = (1/2) * Length of the third 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.

Angle bisectors divide the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

The length of the midsegment is 5, which is half the length of the third side (10).

A perpendicular bisector is the locus of points that are equidistant from the endpoints of a segment.

A point lies on the angle bisector if it is equidistant from the two sides of the angle.