Question

In the given figure, DEFG is a square and ∠BAC = 90º. Show that FG²= BG x FC

Answer 1

DEFG is a square and ∠BAC = 90º =>  FG²= BG x FC

Step-by-step explanation:

∠B = 90° - ∠C   or ∠C = 90° - ∠B

in  Δ BDG

ΔD = 90° - ∠B  = ∠C

& in Δ CEF

∠E = 90° - ∠C = ∠B

now comparing

Δ BDG   & Δ CEF

ΔD  = ∠C

∠B = ∠E

∠G = ∠F  = 90°

=> Δ BDG   ≈ Δ CEF

=> BD/CE  = BG/ EF  = DG/ FC

=> BG/ EF  = DG/ FC

=> BG * FC = EF * DG

EF = DG = FG  ( sides of square)

=> BG * FC = FG * FG

=> BG * FC = FG²

QED

proved

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