Question

prove that altitude of an equilateral Triangles are equal

Answer 1

Answer:

Step-by-step explanation:

Let ABC be the triangle

where AD, BE and CF are the three altitudes on sides BC, AC and AB respectively

In triangle BEC and triangle CFB

angle BEC = angle CFB (both 90o)

angle C = angle B (angles of equilateral triangle are equal)

BC = CB (common)

so, triangle BEC congruent triangle CFB (by AAS congruency)

or BE = CF (by CPCT) -----(1)

similarly, it can be shown that triangle ABE congruent triangle BAD by AAS

and BE = AD (by CPCT) -----(2)

from (1) and (2)

AD = BE = CF