Question

In the following figure, if AD ⊥ BC, then prove that AB² + CD² = BD² + AC².

Answer 1

In right ΔADC,

AC² = AD² + CD²    ...(i)

In right ΔADB,

AB² = AD² + BD²   ...(ii)

Subtracting equation (i) from equation (ii),

AB² – AC² = BD² – CD²

Hence AB² + CD² = AC² + BD² Proved.