In a right triangle ABC right-angled at B, if P and Q are points on the sides AB and AC respectively, then

Given in right triangle ABC right-angled at B, P and Q are points on the sides AB and BC respectively.

Applying Pythagoras Theorem,

In ΔAQB,

⇒ AQ² = AB² + BQ² … (1)

In ΔPBC,

⇒ CP² = PB² + BC² … (2)

Adding (1) and (2),

⇒ AQ² + CP² = AB² + BQ² + PB² + BC² … (3)

In ΔABC,

⇒ AC² = AB² + BC² … (4)

In ΔPBQ,

⇒ QP² = PB² + BQ² … (5)

From (3), (4) and (5),

∴ AQ² + CP² = AC² + PQ²