# prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. using the above theorem prove that a line through the point of intersection of the diagonals and parallel to the base of the trapezium divides the non parallel sides in the same ratio.

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get prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. using the above theorem prove that a line through the point of intersection of the diagonals and parallel to the base of the trapezium divides the non parallel sides in the same ratio. from screen.

## Prove that if a line is drawn parallel to one side of a triangle intersecting the other two side,then it divides the two sides in the same ratio.

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## Prove that if a line is drawn parallel to one side of a triangle intersecting the other two side,then it divides the two sides in the same ratio.

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Updated on : 2022-09-05

Given DE∥BCSolution Verified by Toppr In△ADEand△ABC

∠DAE=∠BAC(commonangle)

∠ADE=∠ABC[∵DE∥BC∴correspondinganglesareequal]

∠AED=∠ACB ∴△ADE∼△ABC Hence AB AD = AC AE

(Insimilartriangle,correspondingsidesareinsameratio)

∵ AB AD = AC AE ⇒ AD AB = AE AC ⇒ AD AB −1= AE AC −1 ⇒ AD AB−AD = AE AC−AE ⇒ AD DB = AE EC ⇒ DB AD = EC AE

It is proved that if a line is drawn parallel to one side of a triangle intersecting the other two side, then it divides the two sides in the same ratio.

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## If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

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

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

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We are given a triangle ABC in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively.

We need to prove that AD/ AE = DB /EC.

Let us join BE and CD and then draw DM

⊥ AC and EN ⊥ AB. Now, area of Δ ADE ( 1/ 2 base × height) = 1/ 2 AD × EN. area of Δ

ADE is denoted as ar(ADE).

So, ar(ADE) = 1/ 2 AD

× EN

Similarly, ar(BDE) = 1 /2 DB

×

EN, ar(ADE) = 1/ 2 AE

×

DM and ar(DEC) =1 /2 EC

× DM.

Therefore, ar(ADE)/ ar(BDE) =

1 2 × AD × EN 1 2 × DB × EN = A D D B --------(1) ar(ADE) / ar(DEC) = 1 2 × AE × DM 1 2 × EC × DM = A E E C -------------(2)

Note that Δ BDE and Δ DEC are on the same base DE and between the same parallels BC and DE.

So, ar(BDE) = ar(DEC) ------------(3)

Therefore, from (1), (2) and (3), we have:

AD/ DB = AE/ EC Suggest Corrections 39

SIMILAR QUESTIONS

**Q.**If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

**Q.**Using Theorem

6.1 ,

prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

**Q.**Prove "If a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

**Q.**If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio

**Q.**Show that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

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## Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

## Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

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