if you want to remove an article from website contact us from top.

    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.

    Mohammed

    Guys, does anyone know the answer?

    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.

    Click here👆to get an answer to your question ✍️ 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.

    Question

    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.

    Medium Open in App

    Updated on : 2022-09-05

    Given DE∥BC

    Solution 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.

    Solve any question of Triangles with:-

    Patterns of problems

    >

    Was this answer helpful?

    134 3

    स्रोत : www.toppr.com

    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.

    Home

    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.

    Question

    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.

    Open in App Solution

    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 ratioQ. 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.

    View More

    स्रोत : byjus.com

    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.

    ← Prev Question Next Question →

    1 Answer

    ← Prev Question Next Question →

    Find MCQs & Mock Test

    Free JEE Main Mock Test

    Free NEET Mock Test

    Class 12 Chapterwise MCQ Test

    Class 11 Chapterwise Practice Test

    Class 10 Chapterwise MCQ Test

    Class 9 Chapterwise MCQ Test

    Class 8 Chapterwise MCQ Test

    Class 7 Chapterwise MCQ Test

    Related questions

    स्रोत : www.sarthaks.com

    Do you want to see answer or more ?
    Mohammed 15 day ago
    4

    Guys, does anyone know the answer?

    Click For Answer