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Question

Consider the following statements:

I. The areas of two similar triangles are in the ratio of the squares of the corresponding medians.

II. The areas of two similar triangles are in the ratio of the squares of the corresponding heights.

Which of the statements given above is/are correct?

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

Both I and II

For two similar triangles, the ratio of their areas equals the square of the ratio of any pair of corresponding linear elements — sides, medians, altitudes (heights), angle bisectors, or circumradii. Hence both Statement I and Statement II are correct.

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Similar Questions

  1. What is the area of quadrilateral ABCD?

  2. ABC is a triangle right angled at B. Let D be the midpoint on AC. If BD = 6.5 cm, then what is AB 2 + BC 2 equal to?

  3. Consider the following statements :

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Important Questions from Triangles, Congruence and Similarity

  1. G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:

  2. If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

  3. What is the area of quadrilateral ABCD?

  4. It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?

  5. Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:

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