Question

In trapezium ABCD, AB parallel CD . AD = BC then show that AB ×CD = AC square- AD square. ​

Answer 1

AB // CD, So AD and BC are the Transerversals. Alternate Interior Angles are equal.

Angle sum property of a quadrilateral

<A + <B + <C +<D = 360

If all angles are equal then all angle is equal to 90 degree.

Now in triangle ACD

By Pythagoras theorem

Square of AD = Square of AC - Square of CD

Which can also be written as,

AD × AD = AC × AC + CD × CD

CD × CD = AC × AC - AD × AD

CD × AB = AC × AC - AD × AD ( CD=AB)

Hence Proved