Question

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Which of the following is true?

• A. AB.BC = AD.DC
• B. AD² + CD² = BD² + AB²
• C. AB² + CD² = BC² + AD²
• D. None of these

Answer 1

The correct option is C

AB² + CD² = BC² + AD²

Since ΔADB and ΔDBC are right triangles, using Pythagoras theorem, we can write

${AB}^2$ = ${AD}^2$ + ${BD}^2$ ------ (1)

${BC}^2$= ${BD}^2$ + ${DC}^2$ ------ (2)

Subtracting (1) and (2) and cancelling out the common terms ( ${DB}^2$), we get, ${AB}^2$ – ${BC}^2$ = ${AD}^2$ – ${DC}^2$. Rearranging, we see that option (c) is correct, ${AB}^2$ + ${CD}^2$ = ${AD}^2$ + ${BC}^2$