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Introduction
We can prove some more properties of triangles using the properties of parallelograms seen in the previous chapter. We find that the line segment joining the mid points of any two sides of the triangle is parallel to the third side and is equal to half of it. We prove this in the mid point theorem.
Midpoint Theorem
The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side.
Converse of Mid-Point Theorem
The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side.
The Intercept Theorem
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
Basic Proportionlity Theorem
A line parallel to one side of a triangle divides the other two sides into parts of equal proportion.
Summary
Midpoint Theorem : The straight line joining the mid-points of two sides of a triangle is parallel to and equal to half the third side.
