The Midpoint Theorem is a fundamental concept in geometry that relates to the properties of line segments. In the ICSE Class 9 Mathematics curriculum, the Midpoint Theorem is typically covered as part of the chapter on Lines and Angles or Triangles. Here’s a summary of the Midpoint Theorem:

**Midpoint Theorem**: In a given line segment, the line segment joining the midpoints of the two sides is parallel to the third side and is half of its length.

**Statement of the Theorem**: Let (AB) be a line segment and (M) be the midpoint of (AB). If (P) is any point on the line segment (AB), then (2 times PM = AB).

**Proof of the Theorem**: The proof involves constructing a parallel line through (P) to (AB), intersecting (AM) and (BM) at points (N) and (O), respectively. Using the properties of parallel lines, it can be shown that (2 times PM = AB).

**Application of the Theorem**: The Midpoint Theorem is used in various geometric proofs and constructions. It helps in understanding the relationship between the sides and diagonals of a triangle and is often used to prove other theorems related to triangles and quadrilaterals.

**Example**: In a triangle (ABC), (D) is the midpoint of (BC). If (AD) is extended to (E) such that (DE = AD), prove that (AB = 2 times DE).

**Conclusion**: The Midpoint Theorem is a fundamental concept in geometry that helps in understanding the properties of line segments and their relationships in geometric figures. It is a key theorem that forms the basis for many other theorems in geometry.