Question

In the given figure if DEFG is a square and ∠BAC= 90° , then show that DE² = BD × EC.

Answer 1

Answer:

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Answer 2

Answer:

In ∆ AFG & ∆DBG

∠GAF = ∠BDG [ 90°]

∠AGF = ∠DBG [corresponding angles because GF|| BC and AB is the transversal]

∆AFG ~ ∆DBG [by AA Similarity Criterion] …………(1)

In ∆ AGF & ∆EFC

∠AFG = ∠CEF [ 90°]

∠AFG = ∠ECF [corresponding angles because GF|| BC and AC is the transversal]

∆AGF ~ ∆EFC [by AA Similarity Criterion] …………(2)

From equation 1 and 2.

∆DBG ~ ∆EFC

BD/EF = DG /EC

BD/DE = DE /EC [ DEFG is a square]

DE² = BD × EC .

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