Mid-point theorem (NF)
A standard method from Quadrilaterals and centres of triangles: the steps and worked examples.
Steps
If M and N are the mid-points of AB and AC, then MN // BC and MN = ½BC.
- Check that both points are mid-points of two sides of the same triangle.
- The segment joining them is parallel to the third side: MN // BC.
- It is half as long as the third side: MN = ½BC. Give the reason (mid-pt. thm.).
Worked examples
Example 1: Mid-point theorem (NF): in △ABC, M and N are the mid-points of AB and AC, and BC = 14 cm. Find MN.
MN = ½ × 14 = 7 cm, and MN // BC (mid-pt. thm.).
For the whole topic, read Quadrilaterals and centres of triangles: key points, common mistakes and how the DSE tests it.