Chapter 6 Triangles Ex 6.4
Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
Since, ∆ABC ~ ∆DEF
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
ABCD is a trapezium with AB || DC and AB = 2 CD
In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that
If the areas of two similar triangles are equal, prove that they are congruent.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(a) 2 :1
(c) 4 :1
Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio
Justification: Areas of two similar triangles are in the ratio of the squares of their corresponding sides.