Question

in triangle ABC, angle B = 90°. prove that AC² = AB² + BC²

Answer 1

This can be proved by phythagores theorem.
First let us draw a perpendicular BD from B to AC.
we get three right angled triangles : ABC, BCD, and ADB
Therefore,
$\frac{AB}{AD} = \frac{AC}{AB} , \frac{AC}{BC} = \frac{BC}{CD}$

AB² = AC·AD , BC² = AC·CD
Adding both,
AB² + BC² = AC·AD + AC·CD
AB² + BC² = AC ( AD + CD )
Since AD+CD=AC
AB² + BC² = AC(AC)
AB² + BC² = AC²
Hence proved

Answer 2

hope this answer is helpful