Q1
The mid-point theorem states the joining segment is:
Aparallel to and half the third side
Bequal to the third side
Cperpendicular to the third side
Ddouble the third side
CBSEClass 9 (CBSE)MathematicsCh 8 · Topic 2
The Mid-point Theorem
Learning the theorem relating midpoints of sides of a triangle.
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The converse of this theorem is also true and useful: if a line is drawn through the midpoint of one side of a triangle, parallel to another side, it will bisect the third side as well. This theorem is frequently applied to prove properties of quadrilaterals formed by connecting the midpoints of another quadrilateral's sides (which always forms a parallelogram, regardless of the original quadrilateral's shape), a surprising and elegant geometric result derived directly from repeated application of the Mid-point Theorem.
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• Mid-point Theorem: the segment joining two side-midpoints of a triangle is parallel to and half the third side.
• The converse is also true: a line through one midpoint, parallel to another side, bisects the third side.
• This theorem helps prove that connecting midpoints of any quadrilateral's sides forms a parallelogram.
• The theorem provides shortcuts for solving midpoint-related geometry problems.