CBSE Class 10 Answered

Draw the triangle as mentioned in the question.

Now consider triangles ADB and AEC.

Both are right triangles according to the information given in the question.

So,

 angle AEC= angle ADB(each is 90 degrees)

angle A = angle A ( common to both triangles)

So,

triangle AEC is similar to triangle  ADB ..(AA similarity)

So,

AE/AD=EC/DB=AC/AB ...( as corresponding sides of similar triangles are proportional)

So,

AE/AD=AC/AB

cross multiplying, we get,

AE*AB=AC*AD

Hence proved.

Note that  it's very important in such questions  to identify which triangles should you consider for similarity.The statement to be proved usually gives a hint on this  matter.