an angle ABC, AB=AC, BD and CE are perpendicular drawn to AC and AB respectively prove that BD=CE​

Question

an angle ABC, AB=AC, BD and CE
are perpendicular drawn to
AC and AB respectively prove that
BD=CE​

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Maria 2 weeks 2021-09-09T16:08:58+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-09T16:10:30+00:00

    Answer:

    <A = <A [Common]

    <ADB = <AEC = 90 deg [As BD & CE are altitudes to the respective sides, by definition of altitudes, the respective angles are 90 deg each]

    Thus the 3rd angles, <ABD = <ACE [By angle sum property of triangles] — (1)

    ii) Thus from the above,

    <A = <A [Common]

    AB = AC [Given]

    <ABD = <ACE [From (1) above]

    So Δ ABD ≅ Δ ACE [ASA congruence axiom]

    If two triangles are congruent, then their corresponding parts are equal.

    So, BD = CE [Proved]

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