Question

In ∆le ABC, LB = 90° BD perpendicular to Ac. prove that AB²+ BC²= AC²


​

Answer 1

answer:

explaination:

∆ABC is similar to ∆ABD

since in similar triangles the ratio of sides are equal.

so,

AB/AC=AD/AB (cross multiplication)

AB²=AC×AD------1.

in the same way,

∆ABC is similar to ∆DBC

so,

BC/AC=CD/BC

BC²=AC×CD------2

add 1+2

AB²=AC×AD

BC²=AC×CD

--------------------

AB²+BC²=AC×AD+AC×CD

AB²+BC²=AC(AD+CD)

AB²+BC²=AC×AC

AB²+BC²=AC²

hence prooved