Mid-Point and Its Converse
ICSE · Class 9 · Mathematics
Quick revision notes for Mid-Point and Its Converse — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Mid-Point Theorem (Theorem 6)
- The line segment joining the midpoints of any two sides of a triangle is parallel to the third side
- This connecting line segment is equal to half the length of the third side
- If D and E are midpoints of sides AB and AC respectively, then DE ∥ BC and DE = ½BC
Converse of Mid-Point Theorem (Theorem 7)
- If a line through the midpoint of one side of a triangle is parallel to another side, it bisects the third side
- This theorem is the reverse of the midpoint theorem
- Used to prove that a point is a midpoint when parallel conditions are given
Applications in Quadrilaterals
- Joining midpoints of adjacent sides of any quadrilateral forms a parallelogram
- In a rectangle, joining midpoints forms a rhombus
- In a parallelogram, the line through midpoints of opposite sides passes through the center
Equal Intercept Theorem (Theorem 8)
- If a transversal makes equal intercepts on three or more parallel lines, any other transversal will also make equal intercepts
- This theorem extends the concept of proportional division to multiple parallel lines
- Used to prove equal divisions without directly measuring lengths
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