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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