Q. 54.4( 136 Votes )
In Fig. 1, DE ll BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar(∆ ABC) to the ar(∆ ADE)?
Answer :
In ∆ ADE and ∆ ABC
∠ ADE = ∠ ABC (Corresponding angles)
∠ DAE = ∠ BAC (same angle)
By AA similarity criteria which states that if two triangles have two pairs of congruent angles, then the triangles are similar.
∆ ADE ≈ ∆ ABC
We know that if two triangles are similar then the ratio of their areas is equal to the square of alternating sides.
The ratio of the ar(∆ ABC) to the ar(∆ ADE) 
Ratio of the ar(∆ ABC) to the ar(∆ ADE) = 9 : 1
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[CBSE 2008]
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