in triangle abc, DE parallel to BC prove ab/ ad = ac / ec ​

Question

in triangle abc, DE parallel to BC prove ab/ ad = ac / ec ​

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Sadie 3 weeks 2021-10-04T00:51:35+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-04T00:52:41+00:00

    Step-by-step explanation:

    Proof: From the figure , ABC and ADE we have

    ABC = ADE …….( Corresponding angles are equal.)

    ACB = AED…….( Corresponding angles are equal.)

    Then by AA axiom of similarity we can conclude that ABC ADE

    We know that corresponding sides of a similar triangles are proportional.

    ∴ AB / AD = AC / AE

    ⇒ ((AD + DB) / AD) = ((AE / EC) / AE) …. (∵ AB = AD + DB and AC = AE + EC)

    ⇒ 1 + (DB / AD) = 1 + (EC / AE)

    ⇒ (DB / AD) = EC / AE

    ⇒ (AD / DB) = AE / EC …..(by taking reciprocals)

    Hence, AD / DB = AE / EC

    0
    2021-10-04T00:53:02+00:00

    Answer:

    Please type the question again..

    It is not clear..

    Whether DE is mid point??

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