In Geometry (Class 9 - Quadrilaterals and Triangles), the Mid-Point Theorem is one of the most important proofs. It reveals a fascinating relationship between the sides of a triangle.
Theorem applies to: Triangles.
Condition: The points must be the exact mid-points of two sides.
Result 1: The joined line is parallel to the third side.
Result 2: The joined line is exactly half the length of the third side.
The theorem states that: "The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it."
Imagine a triangle ABC.
According to the Mid-Point Theorem, two magical things happen to this new line segment DE:
The reverse is also true. If you draw a line from the mid-point of one side (D), parallel to the base (BC), it will automatically hit the exact mid-point of the third side (E).
The mid-point theorem states that the line segment connecting the mid-points of two sides of a triangle is parallel to the third side and is exactly half of its length.
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