Question

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

• A. Any 2 sides of ∆ 1 should be equal to any 2 sides of the ∆ 2
• B. All angles of ∆ 1 should be equal to all angles of ∆ 2
• C. Any 2 sides of ∆ 1 and 1 angle should be equal to any 2 sides and 1 angle of ∆ 2
• D. Any 2 sides of ∆ 1 and including angle should be equal to any 2 sides and including angle of ∆ 2

Answer 1

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 $EF\parallel AB$

Using converse of mid-point theorem,

E is the mid point of BC. [F is mid point of AC and $EF\parallel AB$]

$\Rightarrow EF=\frac{1}{2}AB$

or, $AB=2EF=2\times 3.8cm=7.6cm$