One of the basic question from similarity chapter in which we have been asked to prove that ratio of two sides of triangle are equal.
ML Aggarwal Avichal Publication, chapter 13, question no 14
Rajan@2021Guru
In △ABC,∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB×AE=AC×AD.
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Consider the △ABC,
So, we have to prove that, AB×AE=AC×AD
Now, consider the △ADB and △AEC,
∠A=∠A [common angle for both triangles]
∠ADB=∠AEC [both angles are equal to 90∘]
△ADB∼△AEC
So, AB/AC=AD/AE
By cross multiplication we get,
AB×AE=AC×AD.