△ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Which of the following is true?
AB2 + CD2 = BC2 + AD2
Since ΔADB and ΔDBC are right triangles, using Pythagoras theorem, we can write
AB2 = AD2 + BD2 ------ (1)
BC2= BD2 + DC2 ------ (2)
Subtracting (1) and (2) and cancelling out the common terms ( DB2), we get, AB2 – BC2 = AD2 – DC2. Rearranging, we see that option (c) is correct, AB2 + CD2 = AD2 + BC2