- A7
- B14
- C8
- D6
Step-by-Step Solution
MN joins midpoints of BC and AC, so by the mid-point theorem MN = AB → AB = cm.
Answer: A) 7
In ΔABC, the mid-point of BC is M and the mid-point of AC is N. If MN = 3.5 cm, what is the length of AB (in cm)?
Class 9QuadrilateralsGeometry — Quadrilaterals
Key idea: The mid-point theorem
**Theorem (Mid-Point)**: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
In ΔABC, let D be midpoint of AB and E be midpoint of AC. Then DE ∥ BC and DE = (1/2) × BC.
**Converse**: A line through the midpoint of one side parallel to another side will bisect the third.
In ΔABC, if D is midpoint of AB and a line through D parallel to BC meets AC at E, then E is the midpoint of AC.
**Use**: this theorem solves a huge class of problems where you have midpoints of triangle sides — you can immediately conclude parallelism and half-length.
In ΔABC, let D be midpoint of AB and E be midpoint of AC. Then DE ∥ BC and DE = (1/2) × BC.
**Converse**: A line through the midpoint of one side parallel to another side will bisect the third.
In ΔABC, if D is midpoint of AB and a line through D parallel to BC meets AC at E, then E is the midpoint of AC.
**Use**: this theorem solves a huge class of problems where you have midpoints of triangle sides — you can immediately conclude parallelism and half-length.
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