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Q. The external bisector of an …

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Q. The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

    • Posted by Rohit Kumar 5 years, 2 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Yogita Ingle 5 years, 2 months ago

    Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

    Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.

    Prove that : BD / CD = AB / AC

    Construction : Draw CE || DA meeting AB in E.

    <center cwidth="134" eza="cwidth:134px;;cheight:22px;;wcalc_source:child;wcalc:87px;wocalc:87px;hcalc:22px;rend_px_area:2948;">Statements</center> <center cwidth="350" eza="cwidth:350px;;cheight:22px;;wcalc_source:child;wcalc:64px;wocalc:64px;hcalc:22px;rend_px_area:7700;">Reasons</center>
    1) CE || DA 1) By construction
    2) ∠1 = ∠3 2) Alternate interior angle
    3) ∠2 = ∠4 3) Corresponding angle (CE ||DA and BK is a transversal
    4) AD is a bisector of ∠A 4) Given
    5) ∠1 = ∠2 5) Definition of angle bisector
    6) ∠3 = ∠4 6) Transitivity (from 2 and 4)
    7) AE = AC 7) If angles are equal then side opposite to them are also equal
    8) BD / CD = BA/EA 8) By Basic proportionality theorem(EC ||AD)
    9) BD /CD = AB/AE 9) BA = AB and EA = AE
    10) BD /CD = AB /AC 10) AE = EC and from(7)

    1Thank You

    Krishna Kumawat 5 years, 2 months ago

    Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle. Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.

    1Thank You

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