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The ratio of the the areas of two simila...

The ratio of the the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides/altitudes.

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Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding medians.

Knowledge Check

  • The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides . If DeltaABC~DeltaDEF,BC=3cm, EF=4cm and area of DeltaABC=54cm^(2) , then the area of DeltaDEF is

    A
    `96cm^(2)`
    B
    `106cm^(2)`
    C
    `86cm^(2)`
    D
    `76cm^(2)`

  • The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides . If DeltaABC~DeltaDEF , the area of DeltaABC is 9cm^(2) , the area of DeltaDEF is 16cm^(2)andBC=2.1 cm , then the length of EF is

    A
    2 . 5 cm
    B
    2 . 8 cm
    C
    3 . 2 cm
    D
    3.5 cm

  • If the area of two similar triangles are in the ratio 25:64 find the ratio of their corresponding sides.

    A
    `5:4`
    B
    `3:5`
    C
    `5:8`
    D
    `6:7`

    • Similar Questions

    Explore conceptually related problems

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

    The area of two similar triangles are in ratio of the squares of the corresponding altitudes.

    Theorem 6.6 : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

    The area of two similar triangle are in the ratio of the square of the corresponding angle bisector segments

    Areas of two similar triangles are i the ratio of 4:5, then the ratio of their corresponding sides is :

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