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If the areas of two similar …

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If the areas of two similar triangles are equal, prove that they are congruent

    • Posted by Little Life Love 5 years, 11 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 11 months ago

    Given: ΔABC ~ ΔPQR. &

    ar ΔABC =ar ΔPQR

    To Prove: ΔABC ≅ ΔPQR

    Proof: Since, ΔABC ~ ΔPQR
    ar ΔABC =ar ΔPQR. (given)

    ΔABC / ar ΔPQR = 1

    ⇒ AB²/PQ² = BC²/QR² = CA²/PR² = 1

    [ USING THEOREM OF AREA OF SIMILAR TRIANGLES]

    ⇒ AB= PQ , BC= QR & CA= PR

    Thus, ΔABC ≅ ΔPQR
    [BY SSS criterion of congruence]

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