Question

If a line is drawn parallel to one side of triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. (Prove it).​

Answer 1

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Answer 2

Check The attachment for the proof of the Basic Proportionality Theorem ( BPT ) or Thales Theorem .

Now , Consider a special case :-

From Attachment we have :-

$\quad \qquad \sf \dfrac{AD}{DB} = \dfrac{AE}{EC}$

Adding 1 to both sides ;

${ : \implies \quad \sf \dfrac{AD}{DB} + 1 = \dfrac{AE}{EC} + 1 }$

${ : \implies \quad { \sf \dfrac{AD + DB}{DB} = \dfrac{AE +EC}{EC} }}$

${ : \implies \quad { \sf \dfrac{AB}{DB} = \dfrac{AC}{EC} }}$

On Reciprocal Both sides ;

$\quad \qquad { \bigstar { \underline { \boxed { \red { \bf { \therefore \dfrac{DB}{AB} = \dfrac{EC}{AC} }}}}}}{\bigstar}$

Henceforth , We can say that the sides DB & EC are in same ratio with the full sides AB & AC respectively .

Note :-

Whenever doing these questions in examination . Write these points step by step ;

• Given
• To Prove
• Construction ( If needed )
• Proof/Solution

Always make a suitable diagram . Write the Reason of the Formula used in brackets always like in ( Reason ) , { Reason } & [ Reason ]