Q1
What does the mid-point theorem state?
AThe line joining midpoints is parallel to and half the third side
BThe line joining midpoints equals the third side
CNo relationship exists
DThe midpoints are always equal
ICSEClass 9 (ICSE)MathematicsCh 12 · Topic 1
Mid-Point and Its Converse (Equal Intercept Theorem)
The mid-point theorem states that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its lengt
Core concept
If D and E are midpoints of sides AB and AC of triangle ABC, then DE is parallel to BC and DE = (1/2)BC.
How it works
The converse of the mid-point theorem states that if a line through the midpoint of one side is parallel to another side, it bisects the third side.
Why it matters
The equal intercept theorem relates to parallel lines cutting transversals into proportional segments.
Key detail
These theorems are useful for proving properties of triangles and quadrilaterals, and solving related geometry problems.
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• Mid-point theorem: DE parallel to BC, DE=(1/2)BC.
• D, E are midpoints of AB, AC.
• The converse: a line through one midpoint, parallel to another side, bisects the third.
• The equal intercept theorem involves parallel lines and transversals.
• These prove triangle and quadrilateral properties.
• They help solve related geometry problems.
• These are fundamental coordinate geometry theorems.
• Practice with these builds proof skills.