Question

3. 4.23, if EF || DC || AB. prove that AE/ED=BF/FC​

Answer 1

Step-by-step explanation:

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Answer 2

$\huge\sf\color{pink}\underline{Question}$

if EF || DC || AB. prove that AE/ED=BF/FC

$\huge\sf\color{orange}\underline{Solution}$

Given : AD || DC || AB

To prove : $\dfrac{AE}{ED}$ = $\dfrac{BF}{FC}$

Construction : Join AC

Proof : In ∆ ADC,

=> GE = DC

$\dfrac{AE}{ED}$= $\dfrac{AG}{GC}$...(i) { By basic proportionality theorem }

Now in ∆ ABC,

AB || GF

$\dfrac{CF}{BF}$=$\dfrac{CG}{AG}$

or $\dfrac{BF}{CF}$=$\dfrac{AG}{GC}$....(ii)

From equation (I) and (ii) :-

$\dfrac{AE}{ED}$=$\dfrac{BF}{FC}$