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The Brainliest Answer!

First let us draw a perpendicular BD from B to AC.

we get three right angled triangles : ABC, BCD, and ADB

Therefore,

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