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Chapter 6 · Question 5

What is the theorem on areas of similar triangles?

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Q5

What is the theorem on areas of similar triangles?

Answer Revealed
Direct Answer:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. If △ABC∼△PQR\triangle ABC\sim\triangle PQR, then ar(ABC)ar(PQR)=(ABPQ)2\frac{\text{ar}(ABC)}{\text{ar}(PQR)}=\left(\frac{AB}{PQ}\right)^2.

Simple Explanation

For similar triangles, area ratio is side ratio squared.

Exam-Ready Structure

If two triangles are similar, all corresponding lengths are in the same ratio. Since area depends on two dimensions, the area ratio becomes the square of the side ratio. Thus ar(ABC)ar(PQR)=AB2PQ2=BC2QR2=CA2RP2\frac{\text{ar}(ABC)}{\text{ar}(PQR)}=\frac{AB^2}{PQ^2}=\frac{BC^2}{QR^2}=\frac{CA^2}{RP^2}.

Key Points

  • The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q6

State Pythagoras theorem and its converse.

Q1

What are similar triangles? How are they different from congruent triangles?

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