Question

in the given figure angle a = 90 deg,dgfe is a square. prove fg*fg= bg*fc​

Answer 1

Answer:

proved

Step-by-step explanation:

In the given figure angle a = 90 deg, dgfe is a square. prove fg*fg= bg*fc

In Δ ADE and GBD -----------1

Angle A = angle BGD = 90 degree

Angle ADE = angle DBG (corresponding angles)

By AA postulate

Δ ADE ≅ Δ GBD

In Δ ADE and Δ FEC ----------2

Angle AED = angle FCE (corresponding angles)  

Angle EAD = angle CFE = 90 degree

By AA postulate  

Δ ADE ≅ Δ FEC

From 1 we get

Δ ADE ≅ Δ GBD

From 2 we get

Δ ADE ≅ Δ FEC

Δ GBD ≅ Δ FEC

So GB / FE = GD / FC (since corresponding sides of 2 similar triangles are proportional)

Therefore BG / GF = GF / FC (because FE = GF)

So GF^2 = BG x FC