# In the given figure, DEFG is a square and ∠BAC is a right angle. Show that DE2= BD x EC.

Given: DEFG is a square and BAC = 90°

To Prove: DE2 = BD × EC.

In AGF and DBG

GAF = BDG [each 90°]

AGF = DBG

[corresponding angles because GF|| BC and AB is the transversal]

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

In AGF and EFC

GAF = CEF [each 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), we have

DBG ~ EFC

Since, the triangle is similar. Hence corresponding sides are proportional

[DEFG is a square]

DE2 = BD × EC

Hence Proved

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