Prove the following -In fig if ABCD is a trapezium in which AB- DC - EF then AE-ED-BF-FC OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally

The correct option is D AE/ED=BF/FC In a trapezium ABCD #160; #160;AB∥ DC ∥ EF, WE have to prove, #160; #160; #160; #160; #160; #160 ...

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Standard IX

Mathematics

Trapezium

Prove the fol...

Question

Prove the following :
In fig if ABCD is a trapezium in which $A B ∥ D C ∥ E F t h e n \frac{A E}{E D} = \frac{B F}{F C}$ OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally

\frac{A E}{E D} = \frac{B F}{F C}

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\frac{A E}{A D} = \frac{B F}{F C}

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\frac{A E}{E D} = \frac{B F}{B C}

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None of these

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Solution

The correct option is D $\frac{A E}{E D} = \frac{B F}{F C}$
In a trapezium ABCD $A B ∥ D C ∥ E F,$ WE have to prove, $\frac{A E}{E D} = \frac{B F}{F C}$ Join AC which intersects EF at G
Proof IN $△ C A B, G F ∥ A B$
$∴ \frac{F C}{B F} = \frac{C G}{A G}$ ( Using Thales Theorem)
$\Rightarrow \frac{B F}{F C} = \frac{A G}{C G}$ ....(ii)
(Taking reciprocals)
$△ A D C E G ∥ D C$
$∴ \frac{A E}{E D} = \frac{A G}{G C}$ ....(ii)(By Thales Theorem)
From (i) and (ii) we get $\frac{A E}{E D} = \frac{B F}{F C}$

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Prove the following :In fig if ABCD is a trapezium in which AB∥DC∥EF then AEED=BFFC OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally

Prove the following :
In fig if ABCD is a trapezium in which $A B ∥ D C ∥ E F t h e n \frac{A E}{E D} = \frac{B F}{F C}$ OR Any line parallel sides of a trapezium divides the non-parallel sides proportionally