Question

prove that converse of pythagores thorem​

Answer 1

Step-by-step explanation:

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Answer 2

given: In ΔABC,

           AB²+BC²=AC²

to prove:∠B=90°

construction: draw ΔPQR where PQ=AB AND QR=BC and ∠Q=90°

proof: in triangle PQR,

          ∠Q=90°

           PQ²+QR²=PR²

           AB²+BC²=PR²

 ∴AC²=PR² -------(1)

in ΔABC and ΔPQR,

AB=PQ (by construction)

BC=QR(by construction)

AC=QR (from 1)

∴ΔABC≈ΔPQR

∴∠B=∠Q=90°(C.P.S.T.)