Given,

In ∆PQR,

PD⊥QR,

PQ = a, PR = b, QD = c and DR = d

in right angled ∆PDQ,

PQ² = PD² + QD² [by Pythagoras theorem]

= a² = PD² + c²

= PD² = a² – c² …..(i)

In right angled ∆PDR,

PR² = PD² + DR² [by Pythagoras theorem]

= b² = PD² + d²

= PD² = b² - d² ……(i)

From Equation (i) and (ii),

A² - c² = b² - d²

A² - b² = c² - d²

= (a – b) (a + b) = (c – d) (c + d)

Hence proved.