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