Question

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

Answer 1

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]