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    Question

    State and prove the Pythagoras theorem. (NCERT Class 10, Triangles – Most Important)

    Answer: In right △ABC with ∠B=90°, hypotenuse AC satisfies AC² = AB² + BC². Draw BD ⟂ AC. △ABD ~ △ABC ⇒ AB/AC = AD/AB ⇒ AB²=AC·AD. △CBD ~ △ABC ⇒ BC/AC = DC/BC ⇒ BC²=AC·DC. Adding: AB²+BC²=AC(AD+DC)=AC·AC=AC². Proved.

    Question

    State and prove the Pythagoras theorem. (NCERT Class 10, Triangles – Most Important)

    Answer: In right △ABC with ∠B=90°, hypotenuse AC satisfies AC² = AB² + BC². Draw BD ⟂ AC. △ABD ~ △ABC ⇒ AB/AC = AD/AB ⇒ AB²=AC·AD. △CBD ~ △ABC ⇒ BC/AC = DC/BC ⇒ BC²=AC·DC. Adding: AB²+BC²=AC(AD+DC)=AC·AC=AC². Proved.