Question

In the given figure, DEFG is a square and angle ∠BAC = 90°.
Show that FG² = BG x FC
(CBSE Sample Question Paper Board 2020 Standard).

Answer 1

Step-by-step explanation:

some parts are cut,,but i think it helps you

Answer 2

Hence proved.

Step-by-step explanation:

Given,

A square $EFGD$ and $\triangle ABC$ where $\angle BAC=90$°

In square $EFGD$,

$\angle GDE=\angle FED=\angle EFG=\angle FGD=90$° and

$DE=EF=FG=DG$

In $\triangle BDG$,

$\angle DGB=90$° ( ∵$180-\angle DGF=90$° )

And $\triangle EFC$,

$\angle EFC=90$° (∵ $180-\angle EFG=90$° )

From $\triangle ADE$ , $\triangle BDG$ and $\triangle EFC$ ,

• $\angle DAE=\angle DGB=\angle EFC=90$°

• $DE=BG=FC$
• $\angle DBG=\angle ECF=\angle ADE$ (∵$DE\parallel BC$ )

∴$\triangle ADE$≅$\triangle BDG$≅$\triangle EFC$

Then,

$GF=BG=FC$

∴$FG^{2} =BG\times FC$

Hence proved.