Table of Contents
An Introduction to Midpoint Theorem
Mid Point Theorem:
The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.
Midpoint Theorem Proof
The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.
Proof:
Given: ABC is a triangle with midpoints M, N, and P.
Prove: MN is parallel to BC and has length equal to 1/2 BC.
Step 1: Draw an altitude from point M to side BC. This line, MN, is parallel to BC.
Step 2: Since MN is parallel to BC, it is also the same length as BC.
Step 3: Therefore, MN has length 1/2 BC.
What is the Converse of the Midpoint Theorem?
The converse of the midpoint theorem states that if two points are on a line and the distance between them is equal to the sum of their distances from the two endpoints of the line, then the points are the midpoint of the line.
Uses of Midpoint Theorem
The midpoint theorem can be used in a variety of ways. Some examples include:
- Finding the midpoint of a line segment
- Finding the center of a circle
- Finding the midpoint of a triangle
- Finding the midpoint of a quadrilateral
- Finding the midpoint of a polygon
The Midpoint Theorem
The Midpoint Theorem states that the midpoint of a segment is equidistant from the endpoints of the segment.
The midpoint theorem states that in any triangle, the midpoint of the hypotenuse is equidistant from the vertices. This theorem is easily proven using basic geometry. First, draw the triangle with the given vertices. Next, draw in the midpoint of the hypotenuse. Finally, draw in the perpendicular bisectors of the other two sides. The intersection of the perpendicular bisectors will be the midpoint of those sides.
