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D is the mid-point of side AB of triangle ABC. A line through D is drawn parallel to BC, cutting AC at E.
The carpenter Suresh says E divides AC in the ratio 1 : 1.
What is the ratio AE : EC?

Class 9The Mid-point TheoremGeometry — Quadrilaterals
  • A1 : 1
  • B1 : 2
  • C2 : 1
  • D2 : 3

Step-by-Step Solution

By the converse of the Mid-point Theorem, the line through mid-point D parallel to BC bisects AC, so AE : EC = 1 : 1.
Answer: A) 1 : 1

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