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Home » In ∆ABC, ∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB x AE = AC x AD.
In ∆ABC, ∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB x AE = AC x AD.
CBSE | Class 10 | maths | Maths | ML Aggarwal | Similarity
In ∆ABC, ∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB x AE = AC x AD.

Solution:-

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 90o]

∆ADB ~ ∆AEC

So, AB/AC = AD/AE

By cross multiplication we get,

AB × AE = AC × AD

i

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