Question

In the given figure if DEFG is a square and ∠BAC= 90° , then show that DE² = BD × EC.
(Class 10 Maths Sample Question Paper)

Answer 1

FIGURE IS IN THE ATTACHMENT.

Given: DEFG is a square and ∠BAC = 90°.
To Prove: DE² = BD × EC.
Proof :

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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Answer 2

step by step answer is given in attachments...

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