The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length. CAPS Grade 10 definition, worked example and related geometry practice.
The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
The midpoint theorem says that in any triangle, the line segment joining the midpoints of two sides is parallel to the third side and equal to half of its length. Its converse says that a line through the midpoint of one side, parallel to a second side, bisects the third side.
In △ABC, D and E are the midpoints of AB and AC. If BC = 14 cm, then DE ∥ BC and DE = 7 cm.
Joining the midpoints of the sides of any quadrilateral forms a parallelogram, which you can prove with the midpoint theorem twice.
Midpoint theorem is part of the geometry section of CAPS Grade 10 Mathematics and is examined in Paper 2 of the November exam.
Using the theorem when the points are not midpoints of the sides.
The midpoint theorem says that in any triangle, the line segment joining the midpoints of two sides is parallel to the third side and equal to half of its length. Its converse says that a line through the midpoint of one side, parallel to a second side, bisects the third side.
Midpoint theorem belongs to the Geometry section of CAPS Grade 10 Mathematics, which is examined in Paper 2 of the November exam.
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