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Question

D and F are mid-points of sides AB and AC of ΔABC. A line through F and parallel to AB meets BC at point E. If EF = 3.8 cm, AB =


  1. All angles of ∆ 1 should be equal to all angles of ∆ 2

  2. Any 2 sides of ∆ 1 should be equal to any 2 sides of the ∆ 2

  3. Any 2 sides of ∆ 1 and 1 angle should be equal to any 2 sides and 1 angle of ∆ 2

  4. Any 2 sides of ∆ 1 and including angle should be equal to any 2 sides and including angle of ∆ 2


Solution

The correct option is C

Any 2 sides of ∆ 1 and 1 angle should be equal to any 2 sides and 1 angle of ∆ 2


It is given that EFAB

Using converse of mid-point theorem,

E is the mid point of BC. [F is mid point of AC and EFAB]

EF=12AB

or, AB=2EF=2×3.8 cm=7.6 cm

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