Question

in the given figure d e f is a square and BAC equal to 90 degree show that FG square equals to BD into AC ​

Answer 1

Answer:

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Step-by-step explanation:

wher is the figure

Answer 2

Given - DEFG is a square and ∠BAC = 90⁰

To prove - FG2= BG x FC

Property – If one triangle is similar to the second triangle and the second triangle is similar to the third triangle then the first triangle is similar to the third one.

Answer –

DEFG is a square, therefore we can write,

DE = EF = FG = GD ………(1) (sides of a square)

As opposite sides of square are parallel.

∴ DE || FG

∴ ∠ADE = ∠DBG ………(2) (corresponding angles)

∴ ∠AED = ∠ECF ………(3) (corresponding angles)

As given, ∠BAC = 90⁰

Now, in ∆ADE & ∆GBD,

∠DAE = ∠DGB ………angles of 90⁰

∠ADE = ∠DBG ………from (2)

tri ADE ≈ GBD

………by AA test of similarity

Now, in ∆ADE & ∆FEC,

∠DAE = ∠EFC ………angles of 90⁰

∠AED = ∠ECF ………from (3)

ADE ≈ FEC

………by AA test of similarity

By property, if one triangle is similar to the second triangle and the second triangle is similar to the third triangle then the first triangle is similar to the third one.

As

ADE ≈ GBD

and

ADE ≈ FEC

then

GBD ≈ FEC

GD = BG

FC. EF

………corresponding sides of similar triangles

∴ GD × EF = BG × FC

∴ FG × FG = BG × FC ………from (1)

∴ FG2 = BG × FC

Hence proved !!!

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