The Midpoint Theorem — O/L Mathematics

What must I remember about The Midpoint Theorem?

• The Midpoint Theorem: The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half its length.
• Mathematical statement: In △ABC, if D is the midpoint of AB and E is the midpoint of AC, then DE // BC and DE = (1/2)BC.
• Converse of the Midpoint Theorem: The straight line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side.
• Mathematical converse: In △ABC, if D is the midpoint of AB and line DE // BC, then E is the midpoint of AC (AE = EC).
• Applications in quadrilaterals: The figure formed by joining the midpoints of the consecutive sides of ANY quadrilateral is always a parallelogram.

Test yourself (1 minute)

1. Both halves of the theorem

   Midpoint theorem gives TWO conclusions simultaneously: parallel (DE // BC) AND half-length (DE = 1/2 BC); cite both when needed in proofs.

2. Distinguishing theorem from converse

   Use the theorem when given TWO midpoints; use the converse when given ONE midpoint and ONE parallel line.

3. Rider citation standard

   In Paper 2 Part B geometric proofs, write 'Midpoint theorem' or 'Converse of midpoint theorem' as formal reasons.

Practise The Midpoint Theorem questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 11)

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Grade 11 · Term 2