Question

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

• A. $A{B}^2.B{C}^2=A{D}^2.D{C}^2$
• B. ${AB}^2$ = ${AD}^2$ + ${BD}^2$
• C. ${BC}^2$= ${BD}^2$ + ${DC}^2$
• D. None of these

Answer 1

Answer: (B), (C)

The correct options are
B

${AB}^2$ = ${AD}^2$ + ${BD}^2$

C

${BC}^2$= ${BD}^2$ + ${DC}^2$

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

${AB}^2$ = ${AD}^2$ + ${BD}^2$

${BC}^2$= ${BD}^2$ + ${DC}^2$