1.

In Fig. 5, DEFG is a square and <BAC90°. Show that DE-BDEC.Fig. 5

Answer»

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 ~ ∆EFCBD/EF = DG /ECBD/DE = DE /EC [ DEFG is a square]

DE² = BD × EC

Like my answer if you find it useful!



Discussion

No Comment Found