The Midline Theorem, also known as the Triangle Midsegment Theorem, states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of that side.
To understand this theorem better, consider a triangle ABC. Let D and E be the midpoints of sides AB and AC, respectively. According to the Midline Theorem, the line segment DE connecting points D and E will be parallel to side BC and its length will be equal to half the length of BC. This can be mathematically expressed as:
DE || BC and DE = 0.5 * BC
This theorem is useful in geometric proofs and applications because it establishes a simple relationship between the sides of a triangle using its midpoints. By utilizing the Midline Theorem, one can easily find unknown lengths and prove other geometric properties.