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Mid point theorem and converse

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Mid point theorem and converse

Posted by Vikas Kaul 8 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

Amar Kumar 8 years, 6 months ago

The midpoint theorem states that: In a triangle, the line segment that joins the midpoints of the two sides of a triangle is parallel to the third side and is half of it.

Let us consider ABC is a triangle as shown in the following figure:

Mid Point Theorem
Let D and E be the midpoints of AB and AC. Then line DE is parallel to BC and DE is half of BC;
i.e. DE ∥ BC
DE = 1/2 BC

The converse of midpoint theorem states that: If a line segment is drawn passing through the midpoint of any one side of a triangle and parallel to another side, then this line segment bisects the remaining third side.

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